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).
Rankin’s new well was registered with the North Dakota Industrial Commission as the Abe, after Abe Owan, a local businessman, on whose property Brigham had already installed the Owan, the Abe Owan, and the Owan-Nehring.
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).
The historian Christopher Nehring, who has worked extensively with State Security archives, told German radio, “There is no precedent for State Security to forge an entire dossier, along with the internal bureaucratic forms for registration.”
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.
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).
Nehring
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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