Social Choice

Shifting from the theoretical axioms to applications, we explore basic voting schemes and fair division algorithms.

Elements

1. 4.2.aPlurality Vote

   The ability to select the alternative which is the most preferred one by the largest number of agents (or rank according to the number of individual preferences an alternative is ranked first).

2. 4.2.bBorda Count

   The ability to compute and select the Borda count winner: Borda count is a scheme which, given $m$ alternatives, assigns score $m-i$ to the alternative which is ranked in the $i$'th place by an agent (e.g. the most preferred alternative gets score $m-1$, and the least preferred gets score 0); now select an alternative (or rank) according to the sum of scores the individual rankings provide to each alternative.

3. 4.2.cCopeland's Method

   The ability to compute and select the winner derived by Copeland's method: Each candidate is compared with every other candidate in a series of one-on-one contests. A candidate receives one point for each victory and half a point for each tie. The candidate with the highest total score is the winner.

4. 4.2.dFair Division Algorithms

   The ability to select the correct fair division algorithm given the context (e.g., divider-chooser, last diminisher)

5. Condorcet Winner

   The ability to find the alternative that beats every other in pairwise majority votes, or to recognise that there is none.