The Condorcet jury theorem and extension of?the?franchise with rationally ignorant voters

The Condorcet Jury Theorem (CJT), which provides a justification for democracy, is based on voters who are imperfectly informed insofar as they know the correct policy with a probability of less than one but greater than one-half. We reassess the consequences of the CJT for democracy when extension of the franchise adds equal numbers of non-distinguishable informed and uninformed voters to the collective decision making group. Uninformed voters vote correctly with probability one-half. We show that adding equal numbers of informed and uninformed voters maintains the CJT conclusion that enlarging the group of decision makers increases the likelihood of a correct collective decision.     

Information is important to Condorcet jurors

Group decision making is very significant in a broad variety of settings. This paper deals with committees that make binary decisions and addresses the question of whether informative decisions can be assumed within this framework. We show that when using the optimal decision rule, informative decision making is a Nash equilibrium. Thus we justify the assumption of informative decision making and provide support for the relevance of assumptions such as independent decision making, when using the optimal decision rule.     

Investment Criteria in Single and Multi-Member Economic Organizations

This paper compares the determination of investment criteriain single- and multi-member organizations. Individualdecisional skills are assumed to be endogenous variables thatdepend on the investment criteria. Our main result specifiesthe condition that determines the relationship between theinvestment criteria in single- and multi-member organizations,given the size of the multi-member organization, the decisionrule it applies and the function relating the individual'sdecisional skills to the investment criterion. Theimplications of our main result are developed for specialorganizations such as hierarchies and polyarchies. Ouranalysis implies that the criteria in a multi-memberorganization may be stricter than the criteria set in asingle-member organization, even though in the former case theorganization may worsen the average decision-making ability ofits members. The analysis can be applied not only in singleand multi-member decision making settings, but also in somecontexts of centralized and decentralized decisions. This isillustrated in the case of decisions by editors ofprofessional journals regarding the acceptance or rejection ofsubmitted papers.     

The robustness of the optimal weighted majority rule to probability distortion

This study identifies the optimal collective decision rule in a dichotomous symmetric setting, allowing for probabilities distortion as originally assumed by Tversky and Kahneman (Journal of Risk and Uncertainty 5(4):297–323, 1992). We show that previous results that identified the weighted majority rule as the optimal one, and did not consider subjective probabilities, are robust to such distortion in the sense that neither the rule nor the weights are changed.