Wikipedia acrobatics

A core argument of this weblog is that the checks and balances of the democratic model of Trias Politica fail and that we need an extension with an Economic Supreme Court (ESC) into a Tessera Politica. A government budget tends to be based on forecasts and it is better that those are scientific and hence independent. Economic scientists will forecast what the politicians will do in the future. All kinds of political promises are made, but will they be kept ? What value is a budget, voters will wonder, when it is based upon rosy promises and without scientific scrutiny ? Independence is not enough, the ESC requires the scientific ethic, and be open to society and fellow economic scientists.

This argument causes that this weblog is interested in democracy and in what the public understands about democracy. A friend asked me what I thought about Wikipedia entries on democracy, since that is a source that people tend to refer to with increasing frequency. We actually see some acrobatics here. The subject curves in on itself, like a snake dancer who is able to hold her head by her feet, forming a full circle.

Wikipedia is made by volunteers who apply some notions of democracy themselves to settle differences in approaches. Does the quality of Wikipedia improve with internal democracy ? Have its editors a sound understanding of democracy that is also reflected in what the encyclopedia states about the subject ? Or, do the editors follow what has been written – what they have written themselves ? Might it happen that Wikipedia publishes a wrong analysis on democracy, and that its editors behave in dictatorial fashion ?

Unfortunately, the latter is true: Wikipedia publishes a wrong analysis on democracy, and its editors behave in dictatorial fashion. Wikipedia has been misleading its readers since 2006 because of scientifically unacceptable conduct of its members, and internal rules that allow this. Wikipedia doesn’t show sufficient respect for science, which would be a key requirement for democracy (unless you follow the Trias Politica model where politicians can manipulate science).

The following quotes are from Wikipedia Februari 17 2013 on the entry of Arrow’s impossibility theorem. First note that the article presents a complex mathematical proof. This is needlessly complex. The issue is essentially simpler. Kenneth Arrow gives a general statement, that would apply for all kinds of preferences and situations. Hence it suffices to give a single counterexample to decide to an impossibility. See e.g. the counterexample by Donald Saari, that I copied in DRGTPE at Project Gutenberg.

Thus we arrive at an analysis that most citizens of a democracy could understand: (1) Arrow presents five conditions that would apply to collective decision making in a democracy, (2) There is a contradiction. (3) Thus those five conditions cannot hold all at the same time.

The above can be called “Arrow’s theorem” and it stands (though see below). The confusion starts from that Arrow suggested that the conditions would be “reasonable” and “morally desirable”. This inserts notions of rationality and morality that give a high weight to the discussion. Arrow argues: we must become irrational or immoral if we want to achieve collective decision making, and this will not be “perfect” democracy.

My book “Voting Theory for Democracy” (VTFD) explains that Arrow makes some crucial mistakes here. VTFD is the only book in the world that explains the situation properly. The book turns those “non-mathematical” qualifications “reasonable” and “moral desirable” into mathematics too, such that it casts doubt on the mathematical result.

(a) Reasonable means at least consistent, but his axioms are not consistent. Hence the axioms cannot be called reasonable.

(b) Morality holds that you cannot be obliged to do the impossible. Hence his axioms cannot be morally desirable.

(c) Arrow’s Theorem by their generality would also concern preferences on constitutions. This is a form of self-reference, that his axioms also apply to themselves. Can people have preferences on constitutions ? Yes. The analysis is complete if it covers this intended interpretation. Arrow assumes rational agents but no rational agent would accept his inconsistent axioms. Apparently Arrow’s analysis is incomplete or inconsistent.

Now, where does Wikipedia become misleading ?

(1) Wikipedia-quote: “Although Arrow’s theorem is a mathematical result, it is often expressed in a non-mathematical way with a statement such as “No voting method is fair,” “Every ranked voting method is flawed,” or “The only voting method that isn’t flawed is a dictatorship”. These statements are simplifications of Arrow’s result which are not universally considered to be true. What Arrow’s theorem does state is that a deterministic preferential voting mechanism – that is, one where a preference order is the only information in a vote, and any possible set of votes gives a unique result – cannot comply with all of the conditions given above simultaneously.”

In itself a rather nice synopsis of the situation, except for the points (a) to (c) above. If you assume that Arrow’s axioms would need to be complete with respect to the intended interpretation (are self-referential with respect to constitutions too), then they appear incomplete or inconsistent. 

(2) Wikipedia-quote: “the Gibbard–Satterthwaite theorem still does: no system is fully strategy-free, so the informal dictum that “no voting system is perfect” still has a mathematical basis.”

Here is the same sillyness about “perfection” without a definition about what that would be. Would Arrow’s axioms be the criterion of “perfection”, while we know that they are inconsistent ? If there is no “perfection”, are we to allow people to argue for dictatorship or “let’s accept corruption, since democracy isn’t perfect anyway” ?

Conclusions: (1) Arrow does not study democracy but only a mathematical model, (2) Arrow uses characterisations about that model that cannot be maintained, (3) Arrow breeds cynicism about democracy, (4) many other mathematicians are parrotting this, spreading cynicism about democracy, like speaking about imperfection or even calling for dictatorial mechanisms, (5) Wikipedia neglects the better analysis is VTFD.

The other dismal point is that Wikipedia can show little respect for science and can use dictatorial methods. In 2006 I noticed that an editor had inserted a Wikipedia entry on my suggestion for a Borda Fixed Point voting mechanism. The entry was erroneous at some points, so I took the liberty to correct the Wikipedia entry. In the process I also improved some points on the page on Arrow’s theorem that applies to it. A student in computer science at MIT thought that he had a better understanding of the situation, but was unwilling to show this with logical argument and decent behaviour. See here what followed in terms of gang-rape and witch-hunting. The editors at Wikipedia did not appreciate that I regarded the professors of the student as more relevant for student education than the editors themselves. See here what another student wrote, misleadingly, about the affair. This second student, Joseph Lorenzo Hall now in 2013 has completed his Ph.D. thesis and has become a staff member at the Center for Democracy & Technology. We may wonder what he tells his colleagues about what democracy actually is and how this can be programmed so that we can all benefit from it.

PM 1. The best defence of Wikipedia might be that they base their information on science but that there has been censorship in Holland. But in a case like this you can still think for yourself, and spend some time on the arguments that discussants have given. It helps when you have studied the subject so that you can understand arguments. The subject is democracy and not just a mathematical model.

PM 2. The directorate of the Dutch Central Planning Bureau (CPB) rejected my economic analysis on unemployment and the social welfare function also by referring to Arrow’s Theorem on the impossibility of fair social choice. In response I looked at Arrow’s analysis and wrote a paper that rejected it. However, the CPB directorate did not want to discuss and publish my analysis on Arrow’s theorem either. I have looked for support from outside mathematicians on the analysis in my paper. My position in this discussion has been rather weak since mathematicians refused to look into it or came up with silly remarks and did not respond adequately when I pointed out their own errors. (Dutch readers may look at a summary here.) Resolution of this issue could be very important for understanding my position, and the resolution of the issue of unemployment and social welfare. Yes, economists fail here too, also in the fact that they follow failing mathematicians. Overall, my best advice now is to boycott Holland till the country understands that it has to stop censoring science. Perhaps Wikipedia can write a nice article about that advice to boycott Holland ?

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