2 research outputs found
A Mathematical Model for Optimal Decisions in a Representative Democracy
Direct democracy is a special case of an ensemble of classifiers, where every
person (classifier) votes on every issue. This fails when the average voter
competence (classifier accuracy) falls below 50%, which 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. Representative democracy is a specific way
to improve the ensemble of classifiers. We introduce a mathematical model for
studying representative democracy, in particular understanding the parameters
of a representative democracy that gives maximum decision making capability.
Our main result states that under general and natural conditions,
1. Representative democracy can make the correct decisions simultaneously for
multiple noisy issues.
2. When the cost of voting is fixed, the optimal representative democracy
requires that representatives are elected from constant sized groups: the
number of representatives should be linear in the number of voters.
3. When the cost and benefit of voting are both polynomial, the optimal group
size is close to linear in the number of voters. This work sets the
mathematical foundation for studying the quality-quantity tradeoff in a
representative democracy-type ensemble (fewer highly qualified representatives
versus more less qualified representatives)
Optimal Statistical Hypothesis Testing for Social Choice
We address the following question in this paper: "What are the most robust
statistical methods for social choice?'' By leveraging the theory of uniformly
least favorable distributions in the Neyman-Pearson framework to finite models
and randomized tests, we characterize uniformly most powerful (UMP) tests,
which is a well-accepted statistical optimality w.r.t. robustness, for testing
whether a given alternative is the winner under Mallows' model and under
Condorcet's model, respectively