Decidability in complex social choices

Abstract

Recently, Marengo and Settepanella (2010) introduced a model of social choice among bundles of interdependent elements. In this paper we prove that their voting model is highly decidable, i.e. a group of agents that agrees to use such voting process has an high probability to reach a final decision. We also better qualify the degree of manipulability of such a final decision, showing that it is independent not only from the agenda, but also from the initial condition. Therefore we show that the Marengo and Settepanella (2010) model has nice properties of decidability and can be fruitfully used both for normative and positive analyzes of collective choices among complex interdependent elements.

A graph theoretical approach to decisions in social choice, law, A.I.

“…This allows to retrieve in the automata decisions the concept of local optimum (see the Sect. 4.4) and the result on local optimum obtained in [2] and described in Sect. 3.1.…”

“…Thanks to this graph description Amendola and Settepanella builded an algorithm that allowed them to obtain numerical results described in [1] and to prove (see [2]) that the probability to get a local optimum in the binary case, i.e. f i 's take only value 0 or 1, converge to a value close to 63% when the number of features increases.…”

“…3 in which the vertex 11 is a sink. 2 The aggregation by majority rule gives rise to a cycle involving vertices (0, 0), (0, 1) and (1, 1) corresponding to a cycle between False-False, False-True and True-True. This is a Condorcet cycle which corresponds to the doctrinal paradox (also called discursive dilemma) in Table 2.…”

Towards a unified aggregation framework for preferences and judgments

“…• Social choice on complex multidimensional objects: as already mentioned, one of the interesting properties of our graph-theoretic framework is that it naturally deals with choices on multidimensional alternatives and this enables to encompass the judgment aggregation problem which is inherently multidimensional. Multidimensional social choice has been studied both in many contexts and with different methods (Kramer, 1972) and recently has been analyzed with a graph-theoretic model similar to the one presented in this paper (Amendola and Settepanella, 2012;Marengo and Settepanella, 2014;Amendola et al, 2015), which has produced a series of analytical results on the properties of aggregation and, in particular, on the likelihood to find (and avoid) cycles and on the existence of multiple or unique equilibria. The extension of such results to judgment aggregation seems particularly promising.…”

“…We now show another way to use our core idea that is much less intuitive than our analogies so far. In particular, we are using the idea behind some recent results concerning local and global optima in social choice among multi-dimensional alternatives (Marengo and Settepanella, 2014;Amendola and Settepanella, 2012;Amendola et al, 2015).…”