Electing a committee with dominance constraints
A set of related majority rule-based social choice correspondences are considered: the union of minimal Р-dominating sets MPD (Duggan 2011, Subochev 2016) the union of weakly stable sets MWS (Aleskerov & Kurbanov 1999), the union of minimal P-externally stable sets MPES (Wuffl et al. 1989, Subochev 2008) and the union of minimal R-externally stable sets MRES (Aleskerov & Subochev 2009, 2013). These tournament solutions have not attracted much attention so far. However, the analysis of their properties suggests that MPES and MRES can be useful as instruments of choice, for instance when it is necessary to aggregate rankings. Their implementation is also possible under certain conditions.
The results presented are the following.
1) In a general case of a topological space of alternatives, a sufficient and necessary condition has been provided for an alternative to belong to a minimal P-dominating set. This characteristic condition is related to some version of the covering relation. It has been established that the union of minimal P-dominating sets and the uncovered set are logically nested neither in a general case, nor in finite tournaments. The characterization obtained provides a sufficient condition of nonemptiness of MPES and MRES in a general case of a topological space of alternatives.
2) It has been found that MPES and MRES both satisfy the following axioms:
a) monotonicity with respect to changes in social preferences (P-monotonicity),
b) the generalized Nash independence of irrelevant alternatives,
c) the idempotence,
d) the Aizerman-Aleskerov property,
e) the independence of social preferences for irrelevant alternatives (the independence of losers),
but they do not satisfy the extension axiom (Sen’s property g). It has also been demonstrated that MPD satisfies neither of these axioms, and MWS satisfies P-monotonicity only.
3) It has been found that MPES and MRES both satisfy Sanver monotonicity (a.k.a. cover monotonicity). Thus, despite they are not Maskin monotonic, these social choice correspondences can be implemented in a nonstandard setting, where actors have (extended) preferences for sets of alternatives. It has also been demonstrated that MPD and MWS do not satisfy Sanver monotonicity.
High risk of informal behavior during the Olympic Games bid procedure requires some changes in the current system since the subjectivity in choosing the Olympic Games capital, risk of double selling of the votes and other informal behavior still exist.
Two studies investigated reciprocal effects of values and voting. Study 1 measured adults’ basic values and core political values both before (n=1379) and following (n=1030) the 2006 Italian national election. Both types of values predicted voting. Voting choice influenced subsequent core political values but not basic values. The political values of free enterprise, civil liberties, equality, law and order, military intervention, and accepting immigrants changed to become more compatible with the ideology of the chosen coalition. Study 2 measured core political values before (n=697) and following (n=506) the 2008 Italian national election. It largely replicated the reciprocal effects of voting and political values of Study 1. In addition, it demonstrated that left-right ideology mediated the reciprocal effects of voting and political values. Moreover, voter certainty moderated these effects. Political values predicted vote choice more weakly among undecided than decided voters, but voting choice led to more value change among undecided voters.
We consider the calculation of Nitzan-Kelly’s manipulability index in the impartial anonymous and neutral culture (IANC) model. We provide a new theoretical study of this model and an estimation for the maximal difference between manipulability indices in the IANC model and a basic model, the impartial culture (IC). The asymptotic behavior of this difference is studied with the help of the impartial anonymous culture (IAC) model. It is shown that the difference between the IAC and IANC models tends to zero as the number of alternatives or the number of voters grows. These results hold for any other probabilistic measure that is anonymous and neutral. Finally, we calculate Nitzan-Kelly’s index in the IANC model for four social choice rules and compare it with the IC model.