A Mathematical Model For Optimal Decisions In A Representative Democracy (Lirong Xia)

Abstract

Direct democracy, where each voter case one vote, fails when the average voter competence (classifier accuracy) falls below 50%. This can happen in noisy settings where voters have only limited information, or when there are multiple topics and the average voter competence may not be high enough for some topics. Representative democracy, where voters choose representatives to vote, can be an elixir in both these situations. We introduce a mathematical model for studying representative democracy, in particular understanding the parameters of a representative democracy that gives maximum decision making capability. Under our models we characterize the optimal representative democracy under general and natural conditions.

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