Fractional social choice

Condorcet methods Positional voting Cardinal voting Quota-remainder methods Approval-based committees Fractional social choice Semi-proportional representation By ballot type Pathological response Strategic voting Paradoxes of majority rule Positive results Fractional, stochastic, or weighted social choice is a branch of social choice theory in which the collective decision is not a single alternative, but rather a weighted sum of two or more alternatives.

By contrast, in fractional social choice it is possible to choose any linear combination of these, e.g. "2/3 of A and 1/3 of B".

This mixture can be interpreted as a random variable (a lottery), whose value equals each candidate x with probability p(x).

This lifting process is often called a lottery extension, and it results in one of several stochastic orderings.

Anonymity and neutrality cannot always be satisfied by a deterministic social choice function.

Strategyproofness - reporting false preferences does not lead to a mixture that is better for the voter.

If the preferences are strict, this yields a mixture in which the weight of each alternative is exactly proportional to the number of voters who rank it first.

It satisfies ex-post efficiency, strong SD-strategyproofness, very-strong-SD-participation, agenda-consistency, and cloning-consistency.

In other words, it picks randomly one of the Borde winners (other score functions can be used instead of Borda).

Maximal lotteries - a rule based on pairwise comparisons of alternatives.

This follows from applying the Minimax theorem to an appropriate symmetric two-player zero-sum game.