“One of our oldest residents here is an orangutan named Puppe who just loves to watch people and particularly loves children,” Mr Lentini said.
In each case, the agenda properties are not only sufficient but also (if n ≥ 3) necessary for the result (Nehring and Puppe 2002, 2010; Dokow and Holzman 2010a).
The conjunction of independence and monotonicity is necessary and sufficient for the non-manipulability of a judgment aggregation rule by strategic voting (Dietrich and List 2007c; for related results, see Nehring and Puppe 2002).
The significance of combinatorial properties of the agenda was first discovered by Nehring and Puppe (2002) in a mathematically related but interpretationally distinct framework (strategy-proof social choice over so-called property spaces).
A path-connected agenda (or totally blocked, in Nehring and Puppe 2002): For any p, q ∈ X, there is a sequence p1, p2, …, pk ∈ X with p1 = p and pk = q such that p1 conditionally entails p2, p2 conditionally entails p3, …, and pk−1 conditionally entails pk.
Proposition (Dietrich and List 2007a; Nehring and Puppe 2007): Propositionwise majority voting may generate inconsistent collective judgments if and only if the set of propositions (and their negations) on which judgments are to be made has a minimally inconsistent subset of three or more propositions.
There are many surveys of social choice theory, in broad and restrictive senses: Arrow, Sen and Suzumura (1997, in particular chap. 3, 4, 7, 11, 15; 2002, in particular chap. 1, 2, 3, 4, 7, 10; 2011, in particular chap. 13, 14, 17–20), Sen (1970, 1977a, 1986, 1999, 2009), Anand, Puppe and Pattanaik (2009).
A second variant drops the agenda property of pair-negatability and imposes a monotonicity condition on the aggregation rule (requiring that additional support never hurt an accepted proposition) (Nehring and Puppe 2010; the latter result was first proved in the above-mentioned mathematically related framework by Nehring and Puppe 2002).
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A second variant drops the agenda property of pair-negatability and imposes a monotonicity condition on the aggregation rule requiring that additional support never hurt an accepted proposition Nehring and Puppe 2010 the latter result was first proved in the above-mentioned mathematically related framework by Nehring and Puppe 2002