FAIR-V

First-Approval Instant-Runoff Voting (FAIR-V) is a Single-Winner Cardinal voting systems developed by Aldo Tragni.

The objectives of this voting system is the balance between simplicity, resistance to strategies, and elect the utilitarian winner.

Procedure

Voter score candidates with ratings in [0,3]. Set -1 points to the lowest ratings in each vote (0 to all others).

1. The candidate with the lowest sum of points is eliminated (if in a single vote all candidates with -1 are eliminated, then the remaining candidates with the lowest rating will be set to -1).

Procedures 1 is repeated, until only one candidate remains, who is the winner.

Normalization

Bullet Min Norm: set -1 the minimum value of the ballot to normalize, and the others all to 0.

Using this norm, it's possible to apply the FAIR-V procedure also to ranges with more than 4 ratings.

Name derivation

First-Approval Instant-Runoff Voting:

• "First": refers to the FPTP in which the voter chooses the best candidate to win. In FAIR-V the first choices are such, as long as there are "bad" candidates. After the "bad" candidates have all been eliminated from a ballot, then only the "good" ones are treated as the first choice.
• "Approval": refers to the fact that the voter's first choices can be more than 1, as in AV.
• "Instant-Runoff": refers to the fact that, by eliminating one candidate at a time, only two will remain at the end, obtaining the "Instant-Runoff" (comparison of the top two candidates head-to-head).

FAIR-nV: the FAIR-V norm works with ranges of different sizes and n indicates the number of ratings used in the range, minus 1.

• FAIR-1V: it's equivalent to AV, with ratings in [0,1].
• FAIR-V: is the default definition, with ratings in [0,3].
• FAIR-5V: uses ratings in [0,5].
• FAIR-9V: uses ratings in [0,9].

Strategies resistance

Min-maxing

Properties of FAIR-V:

• increase rating of the candidate X in one vote doesn't change the chance of victory for candidates rated below the old rating of X.
• decreasing rating of the candidate X in one vote doesn't change the chance of victory for candidates rated below the new rating of X.

These properties mean that in FAIR-V a voter cannot favor a candidate more than the worst ones, by increasing his rating.

Example, given this honest vote:
  A[0] B[1] C[2] D[3]   -->   Normalized: A[-1] B[0] C[0] D[0]
if the voter only wanted to increase the chance of victory of B,C,D with respect to A, then vote like this is useless:
  A[0] B[3] C[3] D[3]   -->   Normalized: A[-1] B[0] C[0] D[0]

Voting lesser of two evils

Consider 2 frontrunners F1 and F2, among which the voter considers F1 > F2.

The properties indicated in the previous section ensure that the only interest of the voter is to decrease the rating of F2, leaving the rating of F1 unchanged.

If only F1 and F2 remain at the end of the count, it's sufficient only that those have two different ratings to ensure that the weight of the vote is maximum in favor of F1. This specifically ensures that F1 receives rating 0 if it's the worst candidate among all, or receives 1 if there are candidates much worse than F1 but not frontrunners (minorities); in both cases, the vote would remain very honest.

Monotonicity failure

Using the Yee diagram it was possible to observe that FAIR-V procedure is extremely resistant to the failure of monotonicity, so the Push-over strategy can be considered practically absent.

Voting systems comparison

IRV

IRV assigns 1 point to the candidate with the highest rating, while FAIR-V assigns -1 point to the candidate with the lowest rating; both eliminate at each step the candidate with the lowest sum of points.

A big difference between the 2 types of counting is that in FAIR-V the failure of monotonicity is practically absent, while IRV is one of the systems in which it's most present.

PRO-V

FAIR-V is more resistant to strategies, but has a more complex procedure than PRO-V.