Monday, 25 July 2011

LGS7 - Part I.: Salles on the impossibility of liberalism

I am often annoyed if I miss an interesting conference.  In this post I report on LGS7 – the 7th Conference on Logic Game Theoryand Social Choice, held last week in Bucharest. Of course this post will not help me with missed conferences, but hopefully other game theorists will find them interesting.
There are two types of conferences. The big ones, like the EEA-ESEM meetings, where you can network with a lot of new people, but honestly, with most of them, you are not likely to meet ever again. There are also the small, field conferences, where there is always the risk that you meet all the same people as last year (this can also be nice, too), who give a talk you already know. LGS is the third kind, as it collects people from different disciplines (logicians, game theorists, social choice theorists, but also sociologists, computer scientists) with very specialised interests. As it is organised biannually, it is also unlikely that you will hear an updated version of what you have heard last year.

When I say, I report the conference, I do not promise a comprehensive report – with parallel sessions this would be impossible anyway. This is a subjective report of points that I found interesting.  
As one of the invited speakers, Maurice Salles talked about Rights, Social Choice and Logic. Based on the title the talk could be about practically anything since –with the exception of game theory- all the topics of the conference are listed in the title. The presentation was about the impossibility of being a liberal. The basic idea came from Sen’s paper with a smilar title, and his approach was extended here. First we must clarify what is liberalism. According to Salles liberalism is partial dictatorship, where the individual can, in matters related to him, make decisions disregarding others’ preferences. Weak liberalism, on the other hand, corresponds to a partial veto: if you cannot decide matters for yourself you are at least protected against others deciding for you – again in matters relevant to you. In a sense the first assumes that “I can do whatever I want”, in the second “others cannot make me to do things I do not want”. Then the question can be reformulated in the following way: Is there a –sensible- social welfare function that is compatible with these properties. Under sensibility we mean a set of natural axioms or properties. These properties can be as simple as requiring that if all prefer a to b, then the society should also prefer a to b, but there are also somewhat more complex, but still natural ones, such as the Weak Axiom of Revealed Preferences used by Salles here. The latter claims that if your preference in the supermarket is some food item, then by only allowing you to choose something in the food section you should not alter your preferences and still choose the same item.  Unfortunately even partial veto will not work here.
Salles’s counterexample goes as follows. A and B want to decide who should read LadyChatterley’s Lover. A is prude and prefers that nobody reads it, but if anyone should then B should be saved from the book, and thus prefers to read himself. B is a bit of a pervert, who would like to read it, but would even more enjoy A reading it. So if alternative C is when no-one reads it, A’s preferences are C>A>B, while B’s are A>B>C. Alternative B is quickly eliminated. So the society chooses between letting A or none read the book. This clearly affects A, who would prefer not to read it. While the example is not the best here, since the alternatives A and C have the same implication to B, Salles argued that B has also a say about alternatives A and C. B would of course reject C. In sum, all the alternatives are rejected, so in this simple case there is no social choice function that is compatible with weak liberalism. Salles closed with a quote from John Stewart Mill: “So the Maxims are, first, that the individual  is not accountable to society for his actions, in so far as these concern the interests of no other person, but himself.” The point here is that all actions affect others.

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