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Simplified section on strategies
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First-Approval Instant-Runoff Voting (FAIR-V) is a [[Single Member system|Single-Winner]] [[Cardinal voting systems]] developed by [[User:Aldo Tragni|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 3ratings ratingsin ["good"0,3]. "neutral",Set "bad"]-1 converted,points atto the startlowest ofratings thein counting,each tovote the(0 followingto valuesall [1,1,0]others).
 
# The candidate with the lowest sum of points is eliminated. If(if allin "bad"a candidatessingle arevote eliminatedall fromcandidates awith vote-1 thenare eliminated, in that vote,then the "neutral"remaining candidates arewith setthe tolowest 0rating andwill thebe "good" candidatesset to -1).
 
ProcedureProcedures 1 is repeated, until only one candidate remains, who is the winner.
 
===Normalization===
 
Bmin Norm (Bullet Min Norm): set 0-1 the minimum value of the ballot to normalize, and the others all to 10.
 
Using this norm, it's possible to apply the FAIR-V procedure also to ranges with more than 34 ratings.
 
===Name derivation===
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* "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 amountnumber 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 [0,23].
*FAIR-5V: uses ratings in [0,5].
*FAIR-9V: uses ratings in [0,9].
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===[[Tactical voting#Definitions|Min-maxing]]===
 
Properties of FAIR-V:
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.
* 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.
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.
 
Example, given this honest vote:
A[0] B[1] C[2] D[23] E --> Normalized: A[3-1] FB[50] 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[03] C[03] D[3] --> Normalized: A[-1] B[0] EC[0] FD[50]▼
 
===[[Tactical voting#Voting_for_the_lesser_of_two_evils|Voting lesser of two evils]]===
 
Consider 2 frontrunners F1 and F2, among which the voter considers F1 > F2.
'''2 frontrunners'''
 
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.
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.
 
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.
These are the possible cases of honest voting:
 
===[[Tactical voting#Pushover|Monotonicity failure]]===▼
* 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.
 
Using the [[Yee diagram]] it was possible to observe that FAIR-V procedure is extremely resistant to the failure of monotonicity<ref>{{cite web|url=https://forum.electionscience.org/t/yee-diagramm-strong-monotonicity-failure-resistance/823|title=Strong monotonicity failure resistance|author=Aldo Tragni|language=en|access-date=1 September 2020}}</ref>, so the [[Tactical voting#Pushover|Push-over]] strategy can be considered practically absent.▼
'''4 or more frontrunners'''
 
==Voting systems comparison==▼
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]:
 
===[[IRV]]===
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]
 
[[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.
Overall, FAIR-V is extremely resistant to frontrunners strategies.
 
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.
▲===[[Tactical voting#Pushover|Monotonicity failure]]===
 
▲Using the [[Yee diagram]] it was possible to observe that FAIR-V procedure is extremely resistant to the failure of monotonicity<ref>{{cite web|url=https://forum.electionscience.org/t/yee-diagramm-strong-monotonicity-failure-resistance/823|title=Strong monotonicity failure resistance|author=Aldo Tragni|language=en|access-date=1 September 2020}}</ref>, so the [[Tactical voting#Pushover|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]].
 
==References==
Aldo Tragni
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