The generalized homogeneity assumption and the Condorcet jury theorem

Early expositions and generalizations were proposed by Hoeffding (1956), Grofman (1975), Grofman et al. (1983), Feld and Grofman (1984), Nitzan and Paroush (1982, 1985), Young (1988), Owen et al. (1989), Boland (1989). Ladha (1995) and Berg (1993) relaxed the independence assumption; Austen-Smith and Banks (1996), Ben-Yashar (2006), and Ben-Yashar and Milchtaich (2007) generalized the setting to a strategic voting model; Paroush (1998) emphasized the importance of boundedness away from one-half; Berg and Paroush (1998) studied hierarchical voting. CJT can be generalized to the case of heterogeneous voters. See, for example, Ben-Yashar and Zahavi (2011), Ben-Yashar and Danziger (2011), and Berend and Paroush (1998). Ben-Yashar and Paroush (2000) generalized the non-asymptotic part of the theorem. Berend and Sapir (2005) further generalized the non-asymptotic part of the theorem beyond the analysis of Ben-Yashar and Paroush. Baharad and Ben-Yashar (2009) studied the validity of the CJT under subjective probabilities.

Sah (1991), Sah and Stiglitz (1988) relaxed the symmetry assumption and allowed the decisional skills of each voter to depend on the state of nature. Ben-Yashar and Nitzan (1997) derive the optimal group decision rule in a setting where decision makers’ skills depend on the state of nature.