# The mathematics of whatever you want: some educational content regarding political systems

### My editorial on You Tube

This time, I go educational, and I go educational about political systems, and more specifically about electoral regimes. I generally avoid talking politics with my friends, as I want them to keep being my friends. Really, politics have become so divisive a topic, those last years. I remember, like 20 years ago, talking politics was like talking about the way to organize a business, or to design a machine. Now, it has become more like an ideological choice. Personally, I find it deplorable. There are always people who have more power than other people. Democracy allows us to have some control over those people in power, and if we want to exercise effective control, we need to get your own s**t together, emotionally too. If we become so emotional about politics that we stop thinking rationally, there is something wrong with us.

OK, enough ranting and moaning. Let’s get into facts and method. So, I start as I frequently do: I make a structure, and I drop numbers casually into it, just like that. Later on, I will work through the meaning of those numbers. My structure is a simple political system made of a juxtaposition of threes. There are 3 constituencies, equal in terms of incumbent voters: each constituency has 200 000 of them incumbent voters. Three political parties – Party A, Party B, and Party C – rival for votes in those 3 constituencies. Each political party presents three candidates in the electoral race. Party A presents its candidate A.1. in Constituency 1, candidate A.2. runs in Constituency 2, and Candidate A.3 in Constituency 3. Party B goes sort of the opposite way, and makes its candidates run like: B.1. in Constituency 3, B.2. in Constituency 2, and B.3. in Constituency 1. Party C wants to be original and makes like a triangle: its candidate C.1. runs in Constituency 2, C.2. tries their luck in Constituency 3, and C.3. is in the race in Constituency 1.

Just to recapitulate that distribution of candidates as a choice presented to voters, those in Constituency 1 choose between candidates A.1., B.3., and C.3., voters in Constituency 2 split their votes among A.2., B.2., and C.1.; finally, voters in Constituency 3 have a choice between A.3., B.1., and C.2. It all looks a bit complicated, I know, and, in a moment, you will read a table with the electoral scores, as number of votes obtained. I am just signalling the assumption I made when I was making those scores up: as we have 3 candidates in each constituency, voters do not give, under any circumstance, more than 50% of their votes (or more than 100 000 in absolute numbers) to one candidate. Implicitly, I assume that candidates already represent, somehow, their local populations. It can be achieved through some kind of de facto primary elections, e.g. when you need a certain number of officially collected voters’ signatures in order to register a candidate as running in a given constituency. Anyway, you have those imaginary electoral scores in Table 1, below. Save for the assumption about ‘≤ 50%’, those numbers are random.

Table 1 – Example of electoral score in the case studied (numbers are fictional)

 Number of votes obtained Party Candidate Constituency 1 Constituency 2 Constituency 3 Party A Candidate A.1 23 000 total score [votes]               174 101 Candidate A.2 99 274 Candidate A.3 51 827 Party B Candidate B.1 6 389 total score [votes]               111 118 Candidate B.2 40 762 Candidate B.3 63 967 Party C Candidate C.1 13 580 total score [votes]               134 691 Candidate C.2 33 287 Candidate C.3 87 824 Total 174 791 153 616 91 503

On the whole, those random numbers had given quite a nice electoral attendance. In a total population of 600 000 voters, 419 910 had gone to the ballot, which makes 70%. In that general landscape, the three constituencies present different shades. People in the 1 and the 2 are nicely dutiful, they turned up to that ballot at the respective rates of 87,4%, and 76,8%. On the other hand, people in Constituency 3 seem to be somehow disenchanted: their electoral attendance was 45,8%. Bad citizens. Or maybe just bloody pissed.

Now, I apply various electoral regimes to that same distribution of votes. Scenario 1 is a simple one. It is a strictly proportional electoral regime, where votes from all three constituencies are pooled together, to allocate 5 seats among parties. The number of seats going to each party are calculated as: “Total score of the party/ Total number of votes cast”. Inside each party, seats go specific candidates according to their individual scores. The result is a bit messy. Party A gets 2 seats, for its candidates A.2. and A.3., party B passes its B.3. man, and Party C gets C.3. into the Parliament. The first, tiny, little problem is that we had 5 seats to assign, and just 4 got assigned. Why? Simple: the parties acquired fractions of seats. In the strictly proportional count, Party A got 2,073075183 seats, Party B had 1,323116858, and Party’s C score was 1,603807959. I agree that we could conceivably give 0,32 of one seat to a party. People can share, after all. Still, I can barely conceive assigning like 0,000000058 of one seat. Could be tricky for sharing. That is a typical problem with strictly proportional regimes: they look nice and fair at the first sight, but in real life they have the practical utility of an inflatable dartboard.

Scenario 2 is once again a strictly proportional regime, with 6 seats to distribute, only this time,  in each constituency, 2 seats are to be distributed among the candidates with the best scores. The result is a bit of an opposite of Scenario 1: it looks suspiciously neat. Each party gets an equal number of seats, i.e. 2. Candidates A.2., A.3., B2., B.3., C.2., and C.3. are unfolding their political wings. I mean, I have nothing against wings, but it was supposed to be proportional, wasn’t it? Each party got a different electoral score, and each gets the same number of seats. Looks a bit too neat, doesn’t it? Once again, that’s the thing with proportional: growing your proportions does not always translate into actual outcomes.

Good. I go for the 3rd scenario: a strictly plural regime, 3 seats to allocate, in each constituency just one candidate, the one with the best score, gets the seat. This is what the British people call ‘one past the post’, in their political jargon. Down this avenue, Party A pushes it’s A.2. and A.3. people through the gate, and Party C does so with C.3. That looks sort of fair, still there is something… In Constituency 1, 87 000 of votes, with a small change, got the voters one representative in the legislative body. In constituencies 2 and 3, the same representation – 1 person in the probably right place – has been acquired with, respectively, 99 274, and 33 287 votes. Those guys from constituencies 1 and 2 could feel a bit disappointed. If they were voting in constituency 3, they would need much less mobilisation to get their man past the post.

Scenario 4 unfolds as a mixed, plural-proportional regime, with 5 seats to allocate; 3 seats go to the single best candidate in each constituency, as in Scenario 3, and 2 seats go to the party with the greatest overall score across all the 3 constituencies. Inside that party, the 2 seats in question go to candidates with the highest electoral scores. The results leave me a bit perplex: they are identical to those in Scenario 3. The same people got elected, namely A.2., A.3., and C.3., only this time we are left with 2 vacancies. Only 3 seats have been allocated, out of the 5 available. How could it have happened? Well, we had a bit of a loop, here. The party with the highest overall score is Party A, and they should get the 2 seats in the proportional part of the regime. Yet, their two best horses, A.2. and A.3. are already past the post, and the only remaining is A.1. with the worst score inside their party. Can a parliamentary seat, reserved for the best runner in the winning party, be attributed to actually the worst one? Problematic. Makes bad publicity.

Scenarios 5 and 6 are both variations on the d’Hondt system. This is a special approach to mixing plural with proportional, and more specifically, to avoiding those fractional seats as in Scenario 1. Generally, the total number of votes cast for each party is divided by consecutive denominators in the range from 1 up to the number of seats to allocate. We get a grid, out of which we pick up as many greatest values as there are seats to allocate. In Scenario 5, I apply the d’Hondt logic to votes from all the 3 constituencies pooled together, and I allocate 6 seats. Scenario 6 goes with the d’Hondt logic down to the level of each constituency separately, 2 seats to allocate in each constituency. The total number of votes casted for each party is divided by consecutive denominators in the range from 1 up to the number of seats to allocate (2 in this case). The two greatest values in such a grid get the seats. Inside each party, the attribution of seats to candidates is proportional to their individual scores.

Scenario 5 seems to work almost perfectly. Party A gets 3 seats, thus they get all their three candidates past the post, Party C acquires 2 seats for C.2. and C.3., whilst Party B has one seat for candidate B.3. In a sense, this particular mix of plural and proportional seems even more fairly proportional that Scenario 1. The detailed results, which explain the attribution of seats, are given in Table 2, below.

Table 2 – Example of application of the d’Hondt system, Scenario 5

 Number of votes obtained divided by consecutive denominators Denominator of seats Party A Party B Party C 1 174 101 111 118 134 691 2 87 051 55 559 67 346 3 58 034 37 039 44 897 4 43 525 27 780 33 673 5 34 820 22 224 26 938 6 29 017 18 520 22 449

On the other hand, Scenario 6 seems to be losing the proportional component. Table 3, below, shows how exactly it is dysfunctional. As there are 2 seats to assign in each constituency, electoral scores of each party are being divided by, respectively, 1 and 2. In Constituency 1, the two best denominated scores befall to parties C and B, thus to their candidates C.3. and B.3. In Constituency 2, both of the two best denominated scores are attributed to Party A. The trouble is that Party A has just one candidate in this constituency, the A.2. guy, and he (she?) gets the seat. The second seat in this constituency must logically befall to the next best party with any people in the game, and it happens to be Party B and its candidate B.2. Constituency 3, in this particular scenario, gives two best denominated scores to parties A and C, thus to candidates A.3. and C.2. All in all, each party gets 2 seats out of the 6. Uneven scores, even distribution of rewards.

Table 3 – Application of the d’Hondt logic at the level of separate constituencies: Scenario 6.

 Party A Party B Party C Denominator of seats Constituency 1 1 23 000 63 967 87 824 2 11 500 31 984 43 912 Constituency 2 1 99 274 40 762  (?) 13 580 2 49 637 20 381 6 790 Constituency 3 1 51 827 6 389 33 287 2 25 914 3 195 16 644

Any mechanism can be observed under two angles: how it works, and how it doesn’t. It applies to electoral regimes, too. An electoral regime doesn’t work in two respects. First of all, it does not work if it does not lead to electing anyone. Second of all, it does not work if it fails to represent the votes cast in the people actually elected. There is a term, in the science of electoral systems: the wasted votes. They are votes, which do not elect anyone. They have been cast on candidates who lost the elections. Maybe some of you know that unpleasant feeling, when you learn that the person you voted for has not been elected. This is something like frustration, and yet, in my own experience, there is a shade of relief, as well. The person I voted for lost their electoral race, hence they will not do anything stupid, once in charge. If they were in charge, and did something stupid, I could be kind of held accountable. ‘Look, you voted for those idiots. You are indirectly responsible for the bad things they did’, someone could say. If they don’t get elected, I cannot be possibly held accountable for anything they do, ‘cause they are not in a position to do anything.

Wasted votes happen in all elections. Still, an efficient electoral regime should minimize their amount. Let’s compare those six alternative electoral regimes regarding their leakiness, i.e. their tendency to waste people’s voting power. You can see the corresponding analysis in Table 4 below. The method is simple. Numbers in the table correspond to votes from Table 1, cast on candidates who did not get elected in the given constituency, under the given electoral regime. You can see that the range of waste is quite broad, from 4,8% of votes cast, all the way up to 43% with a small change. It is exactly how real electoral regimes work, and this is, in the long run, the soft spot of any representative democracy. In whatever possible way you turn those numbers, you bump on a dilemma: either the race is fair for the candidates, or the ballot is fair for voters. A fair race means that essentially the best wins. There is no point in making an electoral regime, where inefficient contenders have big chances to get elected. On the other hand, those who lose the race represent people who voted for them. If we want all the voters to be accurately represented in the government, no candidate should be eliminated from the electoral contest, only then it would not be a contest.

Table 4

 Number of votes, which do not elect any candidate Constituency 1 Constituency 2 Constituency 3 Total elections Scenario 1 23 000 40 762 33 287 97 049 Scenario 2 0 13 580 6 389 19 969 Scenario 3 23 000 54 342 33 287 110 629 Scenario 4 63 967 54 342 39 676 157 985 Scenario 5 (d’Hondt method, pooled) 0 54 342 6 389 60 731 Scenario 6 (d’Hondt method, separately by constituency) 23 000 54 342 39 676 117 018 Percentage of votes cast, which do not elect any candidate Constituency 1 Constituency 2 Constituency 3 Total elections Scenario 1 13,2% 26,5% 36,4% 23,1% Scenario 2 0,0% 8,8% 7,0% 4,8% Scenario 3 13,2% 35,4% 36,4% 26,3% Scenario 4 36,6% 35,4% 43,4% 37,6% Scenario 5 (d’Hondt method, pooled) 0,0% 35,4% 7,0% 14,5% Scenario 6 (d’Hondt method, separately by constituency) 13,2% 35,4% 43,4% 27,9% Average 12,7% 29,5% 28,9% 22,4%

I am consistently delivering good, almost new science to my readers, and love doing it, and I am working on crowdfunding this activity of mine. As we talk business plans, I remind you that you can download, from the library of my blog, the business plan I prepared for my semi-scientific project Befund  (and you can access the French version as well). You can also get a free e-copy of my book ‘Capitalism and Political Power’ You can support my research by donating directly, any amount you consider appropriate, to my PayPal account. You can also consider going to my Patreon page and become my patron. If you decide so, I will be grateful for suggesting me two things that Patreon suggests me to suggest you. Firstly, what kind of reward would you expect in exchange of supporting me? Secondly, what kind of phases would you like to see in the development of my research, and of the corresponding educational tools?

# The hopefully crazy semester

Another handful of educational material, for the apparently (hopefully) crazy semester at the university. Crazy because of the virus, stands to reason. Things are never crazy because we make them so, stands to reason, once again.

I am making a big, fat bottom line at my investment portfolio in the stock market, and I am using this opportunity to make some educational material. The point of using my experience in education. It is personal experience, important to enrich theory. It is a story of personal limitations in business decisions, and understanding those limitations is important for understanding microeconomics as the substance of decisions, macroeconomics as their context, and management as their execution.

I have successful experience, together with hindsight on the mistakes I made. I can utilize it as valuable material to share and to build some teaching on. Since January 2020, I have invested  \$7 924,76 in the stock market, and today (August 25th, 2020), my investment portfolio is worth  \$11 719,91. I have 47,89% of return on the cash invested, over a period of 7 months. Not bad for a theoretician, isn’t it? I am deeply convinced that personal experience is impossible to bypass in any true teaching. Whatever kind of story I am telling on the moment, I always tell the story of my own existence. I can make it genuine and truthful just as well. Here is the link to the first, introductory video in this path: ‘My investment experience, my teaching and my science #1’  [Invest 1 2020-08-25 11-54-58 ; https://youtu.be/uYm0xB322u0 ]

In the second video of the same series [Invest 2 2020-08-26 07-37-08; https://youtu.be/XqYbe_LMdhY ], I focus on the presentation of my investment portfolio. I stress two points. Firstly, the portfolio which I hold now is the cumulative outcome of past trials and errors. Secondly, my portfolio shows many alternative scenarios of what could possibly have happened to my money, had I invested in just one among the 27 positions, thus if I had not diversified. I could have made +313% or -49%, instead of the 48% I had made as of August 25th 2020. I study more fundamentally the case of General Electric, which is one of my financial failures as for now. Turns out they have stakes in aviation, and that sucks in the times of pandemic.

In the third video of the series ‘Business Models in the Media Industry’ [Media BM 3 2020-08-26 08-24-42; https://youtu.be/bbmdsTaY7Lg ] I focus more in depth on studying the case of Netflix. You can have a glimpse of their transition from a streamer of externally made content to a business based on in-house made content. You can also see how strongly their business model is grounded in the assumption of constant growth in size.

In my second video devoted to Political Systems [PolitSys 2 2020-08-26 09-02-47; https://youtu.be/iRxwZDKlDxM ] I use two cases, i.e. the constitutions of France and Finland, to give my readers, followers and students a first glimpse on forms of political power. You can see that general concept in the context of distinction between a presidential system (France) vs a Parliamentary one (Finland).

# Business models and the nature of truth – back to school #2

I am introducing another handful of educational content in the form of video tutorials.

The video recorded on August 23rd, noon sharp, is the first in a separate path of teaching devoted to Political Systems. The link to You Tube is here: PolitSys 2020-08-23 11-16-44 (https://youtu.be/J_78zBEFFNE ). The video introduces two case studies: the constitution of Uganda (https://discoversocialsciences.com/wp-content/uploads/2020/08/Uganda-Constitution.pdf ) and the constitution of India (https://discoversocialsciences.com/wp-content/uploads/2019/10/Con-Of-India-updated-as-31072018.pdf ). In terms of theory, two articles are hinted at: Almond, G. A. (1956). Comparative Political Systems. The Journal of Politics, 18(3), 391-409 (https://www.jstor.org/stable/2127255?seq=1 ), and Easton, D. (1957). An approach to the analysis of political systems. World Politics: A Quarterly Journal of International Relations, 383-400 (https://www.jstor.org/stable/2008920?seq=1 ). General concepts which you will find developed in this video are:

>> Constitution as a double-function tool: the set of rules for the political game, and the foundation of the national legal system

>> Constitutional systems as paradoxes: rules of the very brutal political game put together, in the same document, with ambitious ethical principles for the entire nation.

>> The principle of national sovereignty

>> The method of studying constitutions by simulated removal and negation of rules

Material recorded on Monday, August 24th, 2020 (Econ Basics 1 2020-08-24 08-02-06 ; https://youtu.be/OTGjJGfpdoc ) contains the first, more or less formalized lecture in the fundamentals of economics. I use five essential readings – Netflix Annual Report 2019, Discovery Annual Report 2019, Adam Smith’s ‘Wealth of Nations’, David Ricardo’s ‘Principles of Political Economy and Taxation’, and Carl Menger’s ‘Principles of Economics’ – in order to show the basis axes of approach to economic sciences. Firstly, it is the special social tension between the diversity of skills and social roles, on the one hand, and the fact of them all summing up to one big body of labour (Smith). Secondly, I introduce the distinction between capital and labour, and the importance of capital resources (Ricardo, example Netflix). Thirdly, and finally, I present the concept of economic good (Carl Menger) and the importance of translating technology into products.

The video recorded slightly later on August 24th, 2020 (Renew BM 2 2020-08-24 09-35-20; https://youtu.be/VnwLLCDFXS8 ) is the second educational piece in the stream devoted to Business Models in the industry of Renewable Energies. I stay with the two business cases from the first video, i.e. First Solar Inc. and SMA Solar Technology AG, and I focus on connecting their capital accounts – their respective BALANCE SHEETS – to their business models. In terms of the capital base, First Solar is six times bigger than SMA. First Solar’s business model is based, capital-wise, on using retained earnings and additional paid-in capital to finance property, plant, equipment and a large reserve of cash. As regards SMA Solar, they mostly use retained earnings and long-term, complex contractual debt in order to finance factories and large inventories. What emerges as a common denominator between the two is the stream of capital from retained earnings to the financing of fixed productive assets.

In the second video focused on business models in the media industry (Media BM 2 2020-08-24 13-42-46; https://youtu.be/jZKvNfopShM  ), I keep working with two business cases: Netflix, and Discovery Communications. This time, I focus on deconstructing a business model out of the capital account, i.e. from the balance sheet of a company. I present it in the form of a game, which I frequently practice in class with my students: I ask them to identify the biggest numbers (financial aggregates) on both the active and the passive side of the balance sheet. I demonstrate this exercise in this video and explain how you can use the balance sheet to guess the fundamental traits of a business model.

I am also putting online a second video in the educational path devoted to the philosophy of science (Phil Science 2 2020-08-24 14-17-58; https://youtu.be/sCI66lARqAI  ). I am investigating the nature of truth, with three basic readings: Philosophical Essay on Probabilities’ by Pierre Simon, marquis de Laplace, ‘Truth and Method’ by Hans Georg Gadamer, and an article entitled ‘Conscious agent networks: Formal analysis and application to cognition’, by Chris Fields, Donald D. Hoffman, Chetan Prakash, and Manish Singh. I briefly discuss the limitations we, humans, encounter when trying to discover truth about reality.

# The really textbook-textbook exponential growth

### My editorial on You Tube

Here I go again, travelling. Not much of an expedition, just a trip to France, for a family visit of 5 days. As it is usually the case when I go for this type of trip, I am leaving sort of a tiny mess at home. This time, it is a leaking roof, and my son is supposed to handle (hopefully) the professionals, who are supposed (hopefully) to come and fix it.

This is supposed to be a scientific blog, and so I pass to scientific things. I am thinking about two, partly connected topics: my research and teaching about political systems, and a piece of research I am doing on Corporate Social Responsibility, or CSR, in the insurance industry. The connection that I see consists in defining the basic observables in large institutional structures, such as political systems or strongly regulated markets. I mean, how can I sort of know empirically what people do in such structures, with all the foam of propaganda, political and corporate, and with all those metaphysics, based on strong emotions, in the lines of “Corporations always cheat and politicians always cheat!”.

What can I sort of observe empirically, as directly, and as free of bias as possible, in political systems? Two things come to my mind in the first place: legal rules, starting with constitutions, and policies. The latter are partly wrapped in the former, mind you. Then, I am thinking about parties, or coalitions, at power. They are observable through their numerical, electoral scores and the parliamentary seats allotted. In the case of ruling coalitions, the proportions of executive offices, like ministers, deputy ministers, and secretaries of state, held by respective parties in the coalition, can be informative. Now, a little remark: anywhere outside the United States of America, a secretary of state is written in small letters, without capital initials, and means sort of a minister being at the disposition of the prime minister or of the president, inside the structure of respective offices adjacent to those two head jobs. In the United States, the Secretary of State writes himself or herself in with capital initials and is in charge of foreign policy.

As it comes to CSR in the insurance industry, I have three basic observables. One consists of business models, as I can deconstruct them through objective insight into the financials of insurance companies. The other is made of the officially declared policies of social responsibility. Finally, the third observable are the typical contractual patterns applied by insurance companies.

And so I observe those observables. I am strongly quantitative in my approach to anything, and so I am trying to nail down differences across space, as well as changes over time. There is one more thing. Whatever exact avenue I follow, ethics matter. There are certain outcomes of human actions, which can be deemed as social, in the sense of being general and widespread. We are ethical beings, as we want things and strive to achieve goals we see as valuable. If there are any general values, possible to distillate from various goals we are going for, and if these values are essentially constructive and positive, they are ethical values.

Good, that’s theory, and now I am taking on a topic of current importance. The President of my country, Andrzej Duda, has just met President Donald Trump. Apparently, he urged Donald Trump to move American troops from Germany to Poland, and to establish permanent bases of the U.S. military in Poland. That’s what the media say he apparently said he means. This is the foam that I have been just talking about. Now, I am reaching to less foamy a source, namely to the John S. McCain National Defense Authorization Act for Fiscal Year 2019. National Defense Authorisation Acts, voted each year for the next year, are federal peri-budgetary regulations. In the properly spoken Federal Budget of the United States of America, expenditures on defense are essentially presented as discretionary spending, i.e. remaining in the discretion of the executive. Still, the National Defense Authorisation act of each consecutive year gives some detail and some structure to that discretion.

So, in that John S. McCain National Defense Authorization Act for Fiscal Year 2019 three components refer to Poland. Firstly, there is Section 1280, entitled ‘Report On Permanent Stationing of United States Forces in The Republic of Poland. Then, sections 2901 and 4602 give a glimpse of actual expenditures of the U.S. military in Poland, scheduled for 2019. This report is supposed to lay out the feasibility and advisability of permanently stationing United States forces in the Republic of Poland. The type of forces taken into account are both the combat units properly spoken, and the so-called « combat enabler units », i.e. combat engineering, logistics and sustainment, warfighting headquarters elements, long-range fires, air and missile defense, intelligence, surveillance, reconnaissance, electronic warfare.

My experience with studying those things governments do and call ‘policies’ is that governments declare a policy sort of publicly, such as in this case, in an official act, when they have actually already done much in the given direction. In other words, efficient governments do something and then they announce they are going to do it. Inefficient governments declare the willingness to do something, and then they start thinking how the hell they can do it.

And so I go to numbers. Those in the National Defense Authorization Act 2019 come first. Section 2901 specifies the expenditures on Authorized Army Construction and Land Acquisition Projects. As for Poland, it makes a total of \$144 400 000, and it is more than whatever the U.S. Army, the U.S. Navy, or the U.S. Air Force plan to spend in most other countries in Europe. The United Kingdom tops it with \$185 130 000, and Germany closes by, mind you, with \$119 000 000 to be spend by the U.S. Air Force in 2901. Section 4602 contains expenditures grouped under the heading of ‘Military Construction for Overseas Contingency Operations’, and it essentially mirrors the same amount as in Section 2901, i.e. \$144 400 000.

Now, I compare these numbers with their counterparts specified in, respectively, the National Defense Authorization Act for Fiscal Year 2017  – \$8 200 000 to be spent in Poland – and the National Defense Authorization Act for Fiscal Year 2018   >> \$22 400 000 in the same category.

This is an almost textbook case of exponential growth. How do I know it? I take those values for three consecutive years, thus Money(2017) = \$8 200 000, Money(2018) = \$22 400 000, and Money(2019) = \$144 400 000, and I take natural logarithms out of those numbers. Reminder: a natural logarithm is the power, to which the Euler’s constant e = 2,7182 has to be taken in order to obtain the given number. In this case, Money(2017) = e15,91964471, Money(2018) = e16,92457152, and Money(2019) = e18,78532386.

The really textbook-textbook exponential growth is like y = eb*t, where ‘t’ is the number of the consecutive period on a timeline, and ‘b’ is a parameter. Constant exponential growth occurs when the ‘b’ coefficient is constant over time. When ‘b’ dares to grow with each consecutive period, we have an accelerating exponential growth, whose opposite is the decelerating growth with ‘b’ decreasing over time. What I do now is to assume that my three consecutive years are three periods on a timeline, which is basically what they are, but I need to do it sort of by the book, and so I have 2017 = t1, 2018 = t2, and 2019 = t3. Consequently, I divide the natural logarithms from the preceding paragraph by their respective abscissae on the timeline. That gives Money(2017) = e1*15,91964471, Money(2018) = e2*8,462285758, and Money(2019) = e3*6,261774619.

See? The ‘b’ coefficients of this particular exponential chain decrease over time. Here comes the deep logic of exponential growth: it is a type of process over time, where each consecutive step sort of stands and builds up on the shoulders of the preceding steps. Military spending addressed by U. S. Department of Defense, in Poland grows over time but the exponential pace of this growth decreases. The building up over time is impressive in absolute numbers, but it seems to decelerate.

Now, I come back from maths to politics. Those calculations indicate two things. Firstly, whatever is being said in official meetings between my domestic President, and President Trump, regarding the U.S. military presence in Poland, is already happening. The United States are increasing their military footing in Europe in general, and in Poland in particular, and it happens as President Trump loudly declares being sick of it. Secondly, this policy took its strongest kick-start a few years ago, and now it is progressively coming to maturity.

I am consistently delivering good, almost new science to my readers, and love doing it, and I am working on crowdfunding this activity of mine. As we talk business plans, I remind you that you can download, from the library of my blog, the business plan I prepared for my semi-scientific project Befund  (and you can access the French version as well). You can also get a free e-copy of my book ‘Capitalism and Political Power’ You can support my research by donating directly, any amount you consider appropriate, to my PayPal account. You can also consider going to my Patreon page and become my patron. If you decide so, I will be grateful for suggesting me two things that Patreon suggests me to suggest you. Firstly, what kind of reward would you expect in exchange of supporting me? Secondly, what kind of phases would you like to see in the development of my research, and of the corresponding educational tools?

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# A man walks into a bar, and then comes the calm duke

It’s summertime. Politicians are on holiday, hopefully, at least some of them. That’s a good thing, ‘cause when they come to work, like daily, you need to watch them constantly. You turn your back for a second, just for one second, and they come up with something. They are always up to something, those politicians, and so it is good to know what exactly are they up to.

That paragraph, I mean the one above, is an acceptably shitty attempt at the introductory joke for the study of political systems. I do research about political systems, I write serious books about them, and I lecture about them, and I did some blogging about them as well in the past, and so I think I can do some blogging about them now.

Right, so I go on with shitty jokes. A man walks in to a bar, orders a drink, and starts talking to the barman. The man is new in that particular neighbourhood. Such blokes use to ask stupid questions to barmen. This one is no exception to the rule. He goes: ‘Hi, man. Do you have any political system, here?’. The barman is an experienced on. He knows stupid questions, and he is ready to respond. ‘Yes, we do.’ He answers ‘We have a constitution. It proves we have a political system’. ‘You have a constitution? Wow, nice. But, just tell me, how do you know YOU HAVE a constitution? I mean, I understand that part about the constitution as such, but how do you know it is your constitution and not someone else’s constitution?’.

The atmosphere becomes a little tense. What did you expect, man? You ask a man who is serving you drinks how can he know the constitution he thinks is his is really his own. This is bound to raise some eyebrows. Still, the barman holds his ground. ‘This constitution has a rule, written in it, that it is in force in the territory of our country, for one. Besides, it had been enacted, way back in the days, by our Parliament, for two. It all proves it is our constitution, man. Still, good attempt, bravo.’.

‘Yeah, you’re right. If it says it is in force in your territory, it must come from here and be your own. Stands to reason. Good point. But, tell me’ – the man doesn’t give up easily – ‘isn’t it the constitution itself that defines the territory of your country? I mean, it says it is in force in the territory it says is the national territory, doesn’t it? And the Parliament, it is your Parliament because the constitution says so, and the constitution is supposed to be your constitution because it has been enacted by the Parliament it says is the proper Parliament, right? Bit of a conundrum, here, don’t you think?’.

The barman gives up. ‘Look, man. It is nice chatting with you, but I have other customers to attend. See that doorframe over there, on the right? This is Dead Brains’ Room. Go there and ask for Alex. He will tell you more about political systems’.

‘Alex? Alex what?’

De Toqueville. Just go there and ask. The bloke is a fundamentalist, just like you. You should get along well.’

‘A fundamentalist? Me?’

‘Yes. You like asking fundamental questions. C’mon, man. Just go there and talk to Alex’.

The Dead Brain’s Room is a strange collection of people. All kinds of styles, you would say, as if taken from different epochs and places. After asking around, the fundamentalist man finds a slender gentleman with black hair cut into that interesting, like 19th century fashion, where hair on the sides of the head seem to form half-open wings of a bird ready to take flight. He is Alexis de Toqueville. When asked about political systems, he goes into a strange tirade: ‘Amongst the novel objects that attracted my attention during my stay in the United States, nothing struck me more forcibly than the general equality of conditions. I readily discovered the prodigious influence which this primary fact exercises on the whole course of society, by giving a certain direction to public opinion, and a certain tenor to the laws; by imparting new maxims to the governing powers, and peculiar habits to the governed. I speedily perceived that the influence of this fact extends far beyond the political character and the laws of the country, and that it has no less empire over civil society than over the Government; it creates opinions, engenders sentiments, suggests the ordinary practices of life, and modifies whatever it does not produce. The more I advanced in the study of American society, the more I perceived that the equality of conditions is the fundamental fact from which all others seem to be derived, and the central point at which all my observations constantly terminated’.

The fundamentalist man tries to understand. He asked this de Toqueville guy about political systems, and, as an answer, he heard something about equality, course of society, public opinion, laws, governing powers, habits of the governed, the Government with a capital ‘G’, opinions, and sentiments.

The fundamentalist man asks Alexis de Toqueville a few more questions, just to check the background, and here it comes. Now, it makes more sense. Alexis de Toqueville made a long trip to North America, in 1831. He was supposed to visit prisons there, on the request of the French king. So, the guy went to a country completely different from his own, namely the post-Bonapartist France, and he got hooked. Fascination comes from the experience of difference. He became so fascinated with that society under construction, in the early United States of America, that he made a detailed account of the whole system.

Probably without being aware of what he was doing, de Toqueville did an exemplary study of a political system: he started with a historical sketch, just to show how the whole thing came into being, and then he intuitively focused on those aspects of the aspects of the political order. That historical nerve is probably what I appreciate the most in de Toqueville writing. You can notice, by the way, that I have just let go the joke story about that man who walked into a bar, and I am returning to my basic narrative style. That’s the thing, man: you drag a joke over too long a way, and it stops being funny at all.

Anyway, what I like about de Toqueville is his attachment to history, which is even more noticeable given the fact that history, as a real scientific discipline, needed like 2 or 3 decades more to start emerging in the intellectual landscape of Europe. I appreciate the historical approach because I am strongly attached to the idea that social structures in general, political systems included, are very largely made of habits. It is arguable to what extent those habits last over time. The French historical school is, I think, the best at showing how those habits pile up to the point of becoming dysfunctional, and then the social structure shakes off and starts accumulating new habits.

Societies are like hamsters. Each institution, developing over time in the social system, is like another grain of corn that the hamster, i.e. the government, puts in its cheek-bags. Is the hamster stupid? No, not at all. What is does is a very sensible strategy, but it has its limits. Sensible strategies usually do. The limit is the capacity of the hamster’s cheeks. They are not likely to burst, by the way. If you have ever had a hamster, you could see the incredible capacity of that little animal. It can stuff itself up to an insane volume, with that food stored for later. What comes before bursting is impediment in the hamster’s movements. The more you carry in your cheek-bags, the slower and less agile you are, hence the less able to collect new grains. This has been nicely explained by a German mathematician, Reinhard Selten. He was Nobel Prized in economics, together with John Nash and John Harsanyi, and his specific contribution was the theory of games with imperfect recall (see, for example: Selten 1975[1]; Hammerstein, Selten 1994[2]).

Reinhard Selten studied social games played over long periods of time. The law is one of such games. These games have a special trait: the set of players is being changed without interrupting the game. New players come in, and old players drop out. It has to alter the rules of the game, as new players bring with them a word or two about how the game should be played, or, elegantly, they bring new strategies. Now, we have a paradox. Either the coming of new players with new strategies does not change much to the game, in which case we have a rigid social game with not much adaptability, or the game adapts usefully and the new ones alter it with their ideas, but then, the game is not quite the game it used to be. There is a span of time, that Selten used to call as the span of recollection, over which the rules of the game can accommodate both the old players and the new ones. This span is limited. When the discrepancy in expectations and strategies between players who joined at different times reaches a critical point, some old rules naturally drop off the game. Social games played over long periods of time have imperfect recall, because their rules and equilibriums cannot be unequivocally traced back to the hypothetical beginning of the game.

The funny thing about political hamsters is that they like attributing their heritage to things that don’t exist and have never existed. Take the classical partition of three powers, in a government. The legislative should be separate from the executive, and both of them should be accompanied by an independent judicial power. Most people who know a bit of political theory would immediately trace this distinction back to Charles de Secondat, Baron de Montesquieu and his book ‘The Spirit of Laws’. The interesting thing is that when you read that book really carefully, you will not find any mention whatsoever of that principle of division of powers. Montesquieu made a typology of governments, but he did not postulate the division of powers. Who did, then?

Who knows? The separation of the judicial power seems to be of the earliest date, probably due to the progressive emergence of the highly specialized legal profession, century after century. The separation between the executive and the legislative, on the other hand, seems to be an American invention, and to have its roots in the executive offices established in the early British colonies in North America. Read Alexis de Toqueville on that one.

I am getting back to that embarrassing question the fundamentalist man asked to the barman: how can we know we have any political system at all? Is the presence of a constitution a sufficient premise? In general, yes, I agree. Still, there are exceptions. Take Great Britain, for example. Technically, they have a lot of constitutional law without having a written, enacted constitution in the strict sense of the term. I know, I know, there is Magna Charta Libertatum, or The Great Chart of Liberties, from 1215.  I know it feels great to trace the roots of your nation’s constitutional backbone back to the 13th century, but just think of that hamster from the preceding paragraphs. Just how big the cheek-bags of the British political system would have to be in order to carry the institutions collected over more than eight centuries?

Same thing for New Zealand: there is no one, single, compound document called ‘The Constitution of New Zealand’. Still, New Zealand, just as Britain, seems to work quite smoothly, as political systems come. As a matter of fact, I am a huge fan of New Zealand’s political order. They have things, over there, which look really revolutionary, in the positive sense of the term. They have that thing, for example, that the Parliament can vote a budget it has billed like on its own, without any bill from the executive branch.

On the other hand, let’s suppose there is a constitution, but one or more political actors just don’t care, and free ride on the tide of political power. Does it mean there is no political system? Certainly not. If this is not necessarily and strictly speaking the constitution that makes a political system, then what is it? Although the constitutional track is not 100% correct, it gives an insight. Constitution is law, and this law puts order in the intricate network of hierarchies present in the given social structure. Political systems are observable through the lens of laws they enact into force, and through the predictability of behaviour in people who clearly wield power.

Law and predictability of behaviour are connected. Law is made of rules, and, generally, law is law. Still, as you dig deeper, there are two layers in law. In the first place, there is that sort of structural, framework law: the constitution, or, in the absence thereof, the rules regarding the way government should be organized, the civil code, and the criminal one as well, as we talk about codes. You know, that solid stuff that lawyers mean when they tell you in Latin, or almost: ‘Sorry, dude, but ignorantia iuris nocet’ (you get in trouble when you don’t know your law). This layer of law makes the frame of the political system. The presence, and the content, of those laws gives gravitas and predictability to what politicians do.

On the other hand, there are laws oriented on the achievement of a clear purpose, like a plan.  Let’s take a case like from real life. Always embarrassing, to stick close to real life, but always instructive, as well. Recently, Australia has enacted new regulations against espionage, allegedly with the purpose to counter the Chinese interference in the Australian political system. I followed that lead a bit, and I am focusing now on one particular print, namely on the Foreign Influence Transparency Scheme Act 2018 No. 63, 2018. Someone could ask: ‘You are Polish, Mr Wasniewski, so why the hell aren’t you writing about the Polish political system, and instead, you take on those poor Australians?’. Yeah, babe, that’s the thing about writing about political systems. It is frequently safer to write about other countries than about your own. Especially now, in Poland.

Anyway, that second layer of law expresses policies, thus what the political system does. Not all policies are enacted, but many do. It depends on how flexible they are supposed to be, and what about of budgetary money they need. You want a flexible policy that does not necessarily require to divert the stream of taxpayers’ money? You keep it executive, like those presidential proclamations that President Donald Trump uses to impose tariffs on imports. You want to implement a costly policy, which requires fiscal effort, and you don’t really expect to back off in three months from now? In that case you are likely to push some bill through the legislative.

The fundamentalist man enters our bar and asks again: ‘Do you have any political system? How do you know you have any?’. Now, we, the barman, can answer in a little bit more corkscrewed a manner: ‘It depends what kind of political system you fancy, man. If you want something well hinged, sort of regular, with basic legal frame and at least some policies enacted as law, yes, we have plenty. If, on the other hand, you are thinking about something less stringent, rather something sort of like a no-holds-barred game, sorry, we are short of. You can call by that other bar, down the street, with the big « Revolutionary Republic of We Know Better » sign over their door. They should have that second kind on stock, right now. This is probably why you can hear gunshots from there, every now and then’.

All that thinking about political systems made me think of reposting a bit of my writing from last year. It is because I am deeply fascinated with the 17th century in Europe. I have sort of a gut feeling that we are leaving the peaceful world of standardized political systems, which started to build up by the end of the 18th century, and we re-enter the fascinating maze of intertwining social hierarchies of the world, which, fault of a better word, we use to label ‘feudal’. In 1675, the publishing house run by Louis Billaine, located at the Second Pillar of the Grand Salle of the Palace, at Grand Cesar, published, with the privilege of the King, a book entitled, originally, ‘Le Parfait Négociant ou Instruction Générale Pour Ce Qui Regarde Le Commerce’. In English, that would be ‘The Perfect Merchant or General Instructions as Regards Commerce’. The author was Jacques Savary. By the way, the title I provided here above is the abridged one. The full title holds in 13 lines. Master Savary wanted to be precise, and indeed he was. On 829 pages, he covers very comprehensively a lot of practical topics.

I like reading books in a hermeneutic way. It means that I try to deconstruct the context, which the book had been written in. As we are talking 17th century and French monarchy, the most important part of the context could very well be the King, and the king was the Sun King: Louis XIV of France. The second important thing in the context is d’Artagnan. Alexandre Dumas chose to put an end to his hero’s life in 1673, in a battle, identically to the death of the real d’Artagnan, or Charles de Batz de Castelmore d’Artagnan. As we are talking Louis the XIV, we are talking Jean-Baptiste Colbert, the famous minister of finance, and his active, capitalistic policies. We are talking about doing business in an environment strongly marked by the interests of the most powerful people being around. We are talking about the creation of Saint-Gobain, the manufacture of mirrors, today a global business. It was the time, when huge ambitions of the absolutist monarchy went hand in hand with a quick development of really big (I mean bloody big, really) capitalism. There were those first attempts, from the part of the Sun King, of issuing money in order to finance his military prowess. The money in question, later on disdainfully called ‘the Bernardines’, was a failure, but the idea took root (read more in: Sombart 1911 – 2001[3], pages 65 – 70).

So, two years after d’Artagnan’s last battle, and during the reign of the Sun King, Jacques Savary publishes that book about being a perfect merchant, in really mousquetairy an environment. How had he come up with the idea? He states it very frankly in the preface of his book: ‘For although I might have had sufficiently good a name, and sufficiently good a birth, to be employed at some higher profession, I admit that, having been destined for Commerce by my parents, it is the employment, which I occupied myself with for a long time, the care I gave it, the particular cognizance that I took of the most significant and the least things as regards it, the ventures I made with all kinds of Manufactures, the losses that I suffered there, those that I avoided, have given me enough enlightenment and enough experience for ignoring nothing that regards the Negoce’.

I am translating Master Savary’s words the best I can, yet the original is the original. Champagne is a good example. You can get your own PDF of Master Savary’s writing from  www.gallica.bnf.fr , or Bibliothèque nationale de France. Anyway, before I go further in the wording of that preface, I go further hermeneutical with Master Savary. A few interesting things to notice in that first paragraph. ‘Commerce’ and ‘Negoce’ start with capital letters, so I gather it must be something important. Commerce was something slightly different than trade strictly spoken. We are in the world of capitalism based on debt, and more specifically on the bills of exchange. It will take more than an additional century (one and a half, as a matter of fact) to invent the institution of limited liability in a business. Someone could say: in there was no limited liability, it was better to rely on one’s own equity in doing business. Well, yes and no. Yes, because your own equity, contrarily to debt, will not give other people claims on you. No, because if you lose money in a venture, it is, on the whole, better to lose other people’s money than your own. Instead of chipping out of your own possessions, you can borrow money and lend money. The trick, and the art, was to find a balance between lending and borrowing, and it was mostly done with relatively liquid bills of exchange, traded by endorsement.

Those bills of exchange travelled much faster, and changed hands much more frequently than the stocks of goods they were more or less attached to. Commerce was the craft of trading both the goods, and the bills of exchange, at different speeds. Now, comes the subtle shade of Negoce in your Commerce. The merchant called ‘Negociant’ was a really big wholesaler, both in goods and in credit. The Negoce consisted in trading big amounts of goods and capital in a coordinated way. A Negociant could do business for years just by trading credit, without seeing a single barrel of rum or a single sack of corn, or, conversely, he could be an artist in recognizing, for example, good coffee, and making huge deals on it, after sniffing just one handful. A Negociant had to be good in law, in finance, in politics, occasionally in knife fighting, he must have been ready to travel frequently, and to shift elegantly between the crude conditions of an exploration trip and the splendours of Parisian parties. The life of a Negociant was capitalism with its teeth bare and a spark in the eye.

Master Savary says he was well born. He seems suggesting he could afford not to go into Negoce, and yet he did go that way. I guess he must have been the smart guy in the family, but probably not the first in line for inheritance. This is the probable reason why his parents destined him to be a merchant. So he had his teeth cut in doing Commerce, and he must have been really good at it, if, as he writes ‘The cognizance that I had acquired of the practice before being applied to Negoce, stepped from the fact that in the disputes arising ordinarily between Negociants, I endorsed a great number of arbitrages: the advantage I had derived from it is that in the study of evidence, books and personal conduct of those who had recourse to me in their disputes, I made myself sufficiently capable in all the matters the most important and the most difficult in Commerce’.

Yes, Master Savary must have been really quick on the uptake, and smart enough to conceal his speed of thinking a bit, just enough to appear as a steady, reliable arbiter. One thing that remains unclear in this short curriculum, is the order in time. Did he start as an apprentice with a Negociant and gradually became good at arbitrage? Or, maybe, he started as a lawyer and specialized in commercial arbitrage? I do not know. Anyway, he did not stay in the Negoce for ever. ‘The time came when the Commerce was so weakened and bankruptcies so frequent, that there was no security in playing one’s possessions, I judged then that I will do no bad deed by retiring and embracing another profession. An occasion presented itself, which confirmed me in this decision; for a Minister of His Serenissime Highness Monseigneur the Duke of Mantua came in France, who offered me the intendancy of his business in France and Charlville: which I accepted, and entered in the year 1660 to the service of His Serenissime Highness, in which I still am; […]’.

Right, let’s go hermeneutic once again. ‘Serenissime’ means kind of very calm in his ways. Noble born people, in the past, liked dropping this adjective in those long designations, half-name, half-social status that they used to introduce themselves. It probably meant that they wanted to appear cool and relax. ‘Peace, bro. See that Serenissime on my visit card? It means I am really calm, and I will have you executed only at your second mistake. Want a sniff?’. So, Master Savary went into the service of that Italian duke from Lombardy (this is where Mantua is). Being a duke was a good position. The difference between a duke and a prince is that the former is just the top dog in the feudal hierarchy, and the latter is of royal blood and waiting in line for sitting on the throne. Apparently, especially in Italy, being a prince was really unhealthy an occupation. You could have had those horrible hunting accidents, when a wild boar attacked you with five crossbows, and could even follow you home. Waiting in line for top offices is rough. Being a duke was safer, as you were the boss and it was kind of official and legally guaranteed. You just had to wait a few centuries, over some twelve generations, and you had that dukedom. Well, yes, you had to put your bets on the right prince, the one who didn’t get attacked frequently by wild boars with crossbows, or just had more crossbows secured on his side, together with the properly qualified labour force.

So, Master Savary started somehow (?) in the Commerce, then went into business arbitrage, which made him convinced he is really good at Negoce. He went into Negoce, did some business, earned some money, lost some money, and then decided it was not really calm an occupation. When a very calm (i.e. Serenissime) duke from Italy offered him a job, he accepted willingly. As he sketches the job in question, he says: ‘[…] in order to fulfil my obligations it was necessary for me to study the Ordinances and the Customs, as there was much business decisions based thereon; so as I committed myself to read them, and in that reading I made remarks on everything pertaining to Commerce, which served me usefully in the composition of this book. When His Majesty, willing to put a limit, by a Regulation, to the abuses that were being committed in the Negoce, had it ordered by circulating letters to Judges and Consuls, Guards and Communities of Merchants in the good towns of his kingdom to send him their memoirs on this subject, I believed it was my duty to work individually, too, in order to make my eagerness visible and the desire to serve the King and the public; this is why I composed two memoirs, one containing the abuses that were being committed in the Commerce, which I presented to Monseigneur Colbert at the end of August, 1670, the other was a bill of Regulation, which I composed in several chapters, where I proposed dispositions that I saw as just and proper to put a limit all the abuses I mentioned in the first memoire; I presented this bill to Monseigneur Colbert in the following September’.

Right, I am back into hermeneutics. Have you noticed, how long are the sentences in Master Savary’s writing? That was the style of the time, I guess. It survived until the first half of the 19th century, when shorter sentences became definitely the fashion. Did those people, back in the days, have longer breath? Were they able to put more sound between two full stops? Or, maybe, they just have longer and more structured ideas, which they did not feel like truncating? Who knows, they are no longer here to tell us. Anyway, it appears that Master Savary was not really the perfect merchant he wrote about. He had some adventure in the Negoce, but, on the whole, he did not seem to like it. He was more of a bystander to business, who used to have views on business. He was an economist, just as I am. When I was young, I had serious plans for a legal career. In 1989, in Poland, the Big Swing came, everything fell apart, there was not much I could inherit, and so I went into business just in order to survive in the new reality. Doing business was interesting, only I just wasn’t prepared for it, and after fourteen years I decided, just as Master Savary did, to accept a job from a really calm duke. In my case it was a university. Comes the time, comes the calm duke.

Master Savary was an economist, only he did not know he was. The word ‘economist’ comes from the French ‘économiste’, and this was the label put on the followers of Francois Quesnay, the author of ‘The Economic Table’ (French: ‘Tableau économique’), published in 1758, a few years before Adam Smith published his ‘Enquiry Into The Nature and Causes of The Wealth of Nations’. The work by Francois Quesnay was probably among the first piece of macroeconomics officially published, together with ‘The Theory of Taxation’ (French: ‘La Théorie de l’Impôt’) by Marquis de Mirabeau. Initially, the term ‘économiste’ was a bit pejorative and meant some loonies obsessed with numbers. Economics, at the time, the time being the verge of the 18th and the 19th centuries, were ‘political economy’. It was only at the end of the 19th century that any scholar could call himself seriously an economist.

I am an economist, which, due to the work of intellectual titans of the past, is no more equivalent to being a looney obsessed with numbers. Science can help, and this is why I do science.

I am consistently delivering good, almost new science to my readers, and love doing it, and I am working on crowdfunding this activity of mine. As we talk business plans, I remind you that you can download, from the library of my blog, the business plan I prepared for my semi-scientific project Befund  (and you can access the French version as well). You can also get a free e-copy of my book ‘Capitalism and Political Power’ You can support my research by donating directly, any amount you consider appropriate, to my PayPal account. You can also consider going to my Patreon page and become my patron. If you decide so, I will be grateful for suggesting me two things that Patreon suggests me to suggest you. Firstly, what kind of reward would you expect in exchange of supporting me? Secondly, what kind of phases would you like to see in the development of my research, and of the corresponding educational tools?

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[1] Selten, Reinhard. “Reexamination of the perfectness concept for equilibrium points in extensive games.” International journal of game theory 4.1 (1975): 25-55.

[2] Hammerstein, Peter, and Reinhard Selten. “Game theory and evolutionary biology.” Handbook of game theory with economic applications 2 (1994): 929-993.

[3] Sombart, W., 1911-2001, The Jews and Modern Capitalism, translated by M.Epstein, First published 1911, edition 2001 published by Batoche Books Limtied

# Agglutination and ethnocide

### My editorial

Yesterday, in my update in French, I started discussing some literature, which I came by recently, devoted to the issue of quantitative research in long-term social changes (see “La guerre, l’espace, et l’évolution des sociétés” ). As we are talking long-term, this stream of research comes mostly from history. I am currently reviewing one of those papers, entitled ‘War, space, and the evolution of Old World complex societies’ (Turchin et al. 2013[1]). To me, science is, at the end of the day, a method of discovering things. When I see a piece of research done by other scientists, I most of all look for methods. In this precise case, the method is quite illuminating for my own purposes in research. At the baseline of their methodology, Turchin et al. divide big populations in big territories into basic, local cells, equivalent to local communities, and assess three essential probabilities, namely that of coordination occurring between two or more cells, as opposed to the probability of disintegration in such coordinated structures, as well as the probability of at least one cell being destroyed by others. Two other probabilities come as instrumental in calculating the fundamental three: the probabilities of social mutation. Turchin et al. construe the concept of social mutation around that of valuation. At any given moment, there is a set of traits, in a society, which make this society optimally competitive, accounting for requirements stemming from the environment. Any given society develops its own traits through valuating them in its own culture, or, conversely, disintegrates some traits by culturally denying their value. As I understand this methodology by Turchin et al., the concept of valuing some societal traits or disvaluing them is a compound, covering both the strictly spoken ethical valuation, and the actions informative about it (investment, creation or disintegration of specific social structures etc.).

In short, social mutation is supposed to be something akin genetic mutation. There is a set of traits, in a society, and each of those traits can be switched on, or switched off. This is the social code. I am trying to represent it below, in a semi-graphical example, where ‘1’ stands for the given trait being switched on, and ‘0’ to its deactivation.

Trait A     >> 1

Trait B     >> 0

Trait C     >> 0

Trait D     >> 1 etc.

Each society has such a social code, and, in the background, there is some kind of implicitly optimal code, the one that makes the top dog in the pack of societies. The local, social code, observable in any given society displays some Euclidean distance from this optimal code. Putting it simply, in this world, when you are a society, you have all the interest in having the right traits switched on at ‘1’, with the not-quite-favourable ones switched off, i.e. at ‘0’. What Turchin et al. assess, for any given local society studied empirically, is the probability of favourable traits passing from 0 to 1 (µ01: functional mutation), or, conversely, being deactivated from 1 to 0 (µ10: dysfunctional mutation). This specific methodology allows setting baseline probabilities as well. If the general assumption is that societies have a tendency to f**k things up, rather than figuring them out correctly (this is, by the way, what Turchin et al. assume), then µ10 > µ10. If, on the other hand, we have some optimism as for collective intelligence, we can settle for µ10 < µ10. Of course, µ10 = µ10 is a compromise at the weakest possible level of assuming anything. Anyway, the proportions between those probabilities, namely µ01 and µ10, make the overall likelihood for the emergence of large political structures, the ‘ultrasocial’ ones, as Turchin et al. call them (you know: army, taxes, government etc.) in a given set of local communities. Those chances are calculated as: u = ((µ01/(µ01 + µ10)). The ‘u’ symbol comes from that ‘ultrasocial’ adjective. The baseline probabilities in the model, as they come from empirical tests, are: µ01 = 0,0001 and µ10 = 0,002. That makes the likelihood u = 0,05. In other words, in a given set of local communities, a priori not connected by ultrasocial institutions, which, in turn, could stimulate the emergence of political systems, the likelihood that such institutions are triggered on is like 5%.

On the grounds of these findings by Turchin et al., I start my own reasoning. Just hold on to something, ‘cause my reasoning, it can really get some swing, on the account of me having that curious ape inside of me. Anyway, I am translating that tiny u = 0,05 likelihood into the possible behaviour of large human populations living in a territory. Some 5% of those humans, whoever they are, is likely to develop social traits, which can turn them into ultrasocial political systems. This, in turn, means that in every large collection of local communities a relatively small, ultrasocial core is likely to emerge, and this core is going to agglutinate around itself consecutive local communities, to make something really political. Still, the actual empirical results obtained by Turchin et al. are way above those baseline probabilities. The likelihood of turning on the right ultrasocial genes in a given society turns out to be like 0,47 =< µ01 =< 0,51, and the probability µ10 of switching them off ranges from 0,49 to 0,52. That makes the likelihood u = ((µ01/(µ01 + µ10)) floating consistently close to 50%. In other words, if you take 1 million primitive, proto-political people (voters), the baseline likelihood of some among them turning into serious political players, i.e. of turning on the right ultrasocial traits is like µ01 = 0,0001, whilst the probability of them consistently not giving a s***t about going political is µ10 = 0,002, which, in turn, makes that likelihood u = 0,05 of anything seriously political going on in those 1 million people. Now, my internal curious ape spots a detail in the article: those baseline probabilities correspond to something that Turchin et al. call ‘equilibrium’. As an economist, I have a very ground-to-ground approach to equilibriums: it would be nice if they existed in reality, but most of the times they don’t, and we have just a neighbourhood of equilibrium, and still, it is if we are lucky.

I put, now, those two sets of numbers back to back, i.e. the parameters of equilibrium against those empirically inferable from actual historical data. One conclusion jumps to the eye: in real life, we, humans, tend to be some 10 times more prone to do politics in large structures, than we are technically expected to be in the state of equilibrium (whatever is being balanced in that equilibrium). By the way, and to be quite honest in relation to that article by Turchin et al., agglutination around the political core is not the only option actually available. Ethnocide is another one, and, sadly enough, quite recurrent in the historical perspective. Recurrence means, in the results obtained by Turchin et al., a likelihood of ethnocide varying between emax = 0,41 and emax = 0,56 in communities, which had not triggered on their ultrasocial traits at the right moment. This is sad, but seems to be rock solid in that empirical research.

[1] Turchin P., Currie, T.E.,  Turner, E. A. L., Gavrilets, S., 2013, War, space, and the evolution of Old World complex societies, Proceedings of The National Academy of Science, vol. 110, no. 41, pp. 16384 – 16389