Fractional social choice

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Fractional social choice^[1] 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. For example, if society has to choose between three candidates: A B or C, then in standard social choice, exactly one of these candidates is chosen, while in fractional social choice, it is possible to choose (for example) "2/3 of A and 1/3 of B".

A common interpretation of the weighted sum is as a lottery, in which candidate A is chosen with probability 2/3 and candidate B is chosen with probability 1/3. Due to this interpretation, fractional social choice is also called random social choice,^[2] probabilistic social choice,^[3] or stochastic social choice.^[4] But it can also be interpreted as a recipe for sharing, for example:

• Time-sharing: candidate A is (deterministically) chosen for 2/3 of the time while candidate B is chosen for 1/3 of the time.
• Budget-distribution: candidate A receives 2/3 of the budget while candidate B receives 1/3 of the budget.
• Fair division with different entitlements can also be used to divide a heterogeneous resource between candidates A and B, with their entitlements being 2/3 and 1/3.