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 utilitarian winner.

Procedure

Voter score candidates with 3 ratings ["good", "neutral", "bad"] converted, at the start of the counting, to the following values [1,1,0].

1. The candidate with the lowest sum of points is eliminated. If all "bad" candidates are eliminated from a vote then, in that vote, the "neutral" candidates are set to 0 and the "good" candidates to 1.

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

Normalization

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

Using this norm, it's possible to apply the FAIR-V procedure also to ranges with more than 3 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 amount 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 [0,2].
• FAIR-5V: uses ratings in [0,5].
• FAIR-9V: uses ratings in [0,9].

Strategies resistance

Min-maxing

The min-maxing strategy in general consists of giving some candidates the lowest rating, and others the highest. If the voter is undecided about some candidates, then he will give them the rating in the middle.

Focusing ratings on the extremes and on the middle is exactly what voters already do in the FAIR-V honest vote, so the min-maxing strategy will generate tactical votes almost equal to the honest ones.

Voting lesser of two evils

2 frontrunners

Only 2 frontrunners F1 and F2 are considered, among which the voter considers F2 worse than F1. The strategy is always to make sure that F1 has a higher rating than F2.

These are the possible cases of honest voting:

• F1[neutral] F2[bad] or F1[good] F2[bad]: if F2 is already "bad" in the honest vote, then there are no strategies.
• F1[good] F2[neutral]: also in this case, the "bad" candidates are considered worse than F2 and are hypothetically minorities (not frontrunners). In this context it makes sense that F2 is left in "neutral", in order to make sure that the "bad" candidates are eliminated before the others, and once they are all eliminated, the vote will only support F1 against F2.
• F1 and F2 with the same rating: only in this case, the ratings of F1 and F2 may change. However, the rating is changed in respect of the voter's interests. Eg if F1 and F2 are "neutral" the voter can move F1 to "good" or F2 to "bad", according to his interests.

4 or more frontrunners

Now consider the case in which the frontrunners are 4 or more, which is a more realistic context. FAIR-V, using range with only 3 ratings, the voter is forced to provide an honest vote regarding frontrunners. This positive side can be seen by making a comparison with methods that use ranking or range[0,5]:

A,B,C,D,E,F are only frontrunners (there are also hidden minority candidates).
2 votes with utility in [0,1000]:
    A[340] B[400] C[570] D[780] E[810] F[900]
    A[20]  B[160] C[310] D[400] E[530] F[1000]
Votes with rank (equal, although the utility is very different)
    A > B > C > D > E > F
Honest vote with ranges [0,5]
    A[2] B[2] C[3] D[4] E[4] F[5]
    A[0] B[1] C[2] D[2] E[3] F[5]
Tactical vote with ranges [0,5]
    A[0] B[0] C[0] D[5] E[5] F[5]
    A[0] B[0] C[0] D[0] E[0] F[5]
FAIR-V honest votes
    A[0] B[1] C[1] D[2] E[2] F[2]
    A[0] B[0] C[0] D[1] E[1] F[2]
FAIR-V tactical votes
    A[0] B[0] C[1] D[2] E[2] F[2]
    A[0] B[0] C[0] D[1] E[1] F[2]

Overall, FAIR-V is extremely resistant to frontrunners strategies.

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

PRO-V

FAIR-V is more resistant to strategies using range [0,2], but has a more complex procedure than PRO-V.