So you are actually describing two procedures here, either of which could be chosen for an election before it is held, as part of the election design, right? The choice would be of your overall procedure with a fixed decision about which tie-breaking variant to use, in advance of the election.
(apart from the rare cases of ties)
It sounds to me as though ties would be common. Scores that could tie are from numbers of candidates, which could be three, rather than from numbers of voters, which can be in the millions, and rather than from scores added up from voters.
I believe Condorcet cycles are fairly heard of or expected, although I suppose they occur less than half the time, maybe less than a tenth of the time, I don't know. For example among four candidates, we could have that A beats B and D, B beats C and D, C beats A and D, and D beats no one. So the scores would be 2, 2, 2, 0, a three-way tie.
My first thought with respect to any newly proposed voting system is to examine the question of whether the system provides tit-for-tat balance.
I believe the first part of your system, the part up to but excluding the tie-breaking subprocedure, does provide balance. This first part considers the possible pairings of candidates. The obvious antivote to a given vote would invert the grades assigned to the candidates. Best would become Worst, Worst would become Best, 4 and 1 would be interchanged, and 2 and 3 likewise. Such an antivote would decide between any two candidates in the opposite way as the original vote. Since the outcome of the first part of the procedure depends wholly on which candidate wins each pairing, the procedure up to but excluding the tie-breaking aspect does provide tit-for-tat balance.
So, let's look at the tie-breaker. I think one of your tie-breaker variants is more IRV-like, and the other is more Coombs-like. I will just examine the latter, as I think they are enough alike that both do or do not provide balance.
Only the 2 candidates (among those in tie) with the lowest number of ratings [worst] are considered, among which the one who won in the pairwise match wins.
I will concentrate on
Only the 2 candidates (among those in tie) with the lowest number of ratings [worst] are considered,
This means that the antivotes I considered before, are not necessarily antivotes for this part of the procedure. The candidates who received Worst in a proposed antivote are those who received Best in the original vote, which has nothing to do with the determination of who is considered. So, the tie-breaking procedure and the system as a whole fails Tit-for-Tat. So, I suspect it smacks too much of the antidemocratic characteristics of FPtP. This is a consideration of power relations, so trumps the strategic help, I would say.
In devising KP Voting I did not start out by articulating to myself in so many words, that I was trying to provide a strategy that depended to a lesser degree on the background information of the election. However, in an indirect way, that was part of the real motivation, because I believe that IRV advocates believe that IRV does just that, and I was trying to incorporate IRV so that the system could attract acceptance from IRV advocates and Approval advocates. So, maybe you can judge KP as moving in the direction you seek, when it is compared to Approval.
For tie-breaking, I propose that among the candidates in the tie, the one who wins a Score election from the original ballots wins the election. Best would count as 5, and Worst would count as zero. But if a ballot did not use the full range once the eliminated candidates are struck from it, it is linearly expanded to use the full range.
Assuming to use tie procedure 2, the worst that can happen in the case of cycles is that some of the few candidates belonging to the cycle receive [worst] instead of intermediate ratings.
This is if the voter can predict that there will be a cycle and which candidates will belong to it (it's not easy).
If they don't know which candidates belong in the cycle, then minimizing is very risky because it also remains true that in case of not tie, minimizing to [worst] is senseless.
Given these votes:
A [best] B  C  D [worst]
A [worst] B  C  D [best]
When it comes to the management of the tie (procedure 1), the 2 candidates with the most [best] are held, so A and C are in tie.
With tie procedure 2, the 2 candidates with least [worst] are held which are B and C, which however result in tie (if there was only B, I would have to keep B and one between A and C in tie).
You always end up with a tie (it makes sense), even if there is still an imbalance towards certain candidates (those with intermediate ratings) rather than towards others.
However, tit-for-tat is not a criterion that I value very much (and I also point out that it only fails in the case of tie, otherwise it's satisfied, unlike FPTP which always fails).
Score for tie
If I use Score, I introduce the min and max strategies in case of tie, while with my procedure only one of the 2 strategies can be valid in case of tie.
I will inquire about KP voting.
I have read KP and partly agree.
You look for a half way between IRV and AV.
S-TM instead is an half way to other methods:
- If everyone in S-TM voted with [worst] and [best], it would become AV.
- If everyone in S-TM voted with intermediate ratings, it would become Score.
- Condorcet (pairwise comparisons) to mix AV and Score.
- in case of tie, all candidates but 2 are eliminated on which the comparison is then made , similar to STAR.
multi_system_fan last edited by
what exactly do the letter S-TM stand for?
multi_system_fan last edited by multi_system_fan
Am I right in suspecting that both in S-TM1 and S-TM2 there could be ties that are not resolved with the suggested Tie-breaking rules.
For instance for S-TM1 : when there are 20 candidates and 5 of them have the same sum of (adjusted )scores while 3 of them have also the same number of ratings [best] and 2 of them also have the same number of ratings [ worst]
multi_system_fan last edited by
- add something like: this is intended as a single winner method
- "The candidate who wins in the most pairwise matches wins." better: "The candidate with the highest sum of points wins"
@Essenzia I see what you are saying but this normalization is complex. The STLR is simpler to understand and would help people vote better. STLR comes with a clear and clean scale.
Yes, there are unresolved tie cases as in any voting method. The important thing is that they are sufficiently rare.
If 1000 or more voters vote, it is extremely rare that multiple candidates have the same number of [best] or [worst] just as it is extremely rare in AV that multiple candidates have the same number of votes.
Frequent tie cases to be solved are those caused by condorcet cycles and for those the solution is proposed.
"The candidate with the highest sum of points wins" is not the method I am proposing. With a similar process, there could be many more min-max strategies.
The benefits of STLR and STAR fall with the clones, becoming Score Voting. I don't think the added complexity of such methods is worth it in the long run (given that in the long run, political factions would understand this clone problem and exploit it to their advantage).
@Essenzia I do not think that the clone problem can be exploited. There will always be an individual who wants to win. If there was two candidates supported by the largest bloc of about 40% of the voters they would still fight with eachother. They would try to find more and more supporters by adjusting their platform. This means that it is not a Nash equilibrium and that the candidates would drift towards more and more support.
It is important to realize that in a system without vote splitting the power of parties would be greatly reduced.
Also, falling back to score is not something I would view as a problem.
@Keith said in S-TM:
If there was two candidates supported by the largest bloc of about 40% of the voters they would still fight with eachother.
Yes, but they would still both be supported by that 40% because they both don't want to do things that make them lose that block.
Positive the fact that they try to have the block bigger and bigger, but if the block is for example "Republican", it will remain "Republican" (as well as the 2 candidates who then end up in the automatic runoff).
Also, falling back to score is not something I would view as a problem
The problem is that if you end up in Score Voting then you might as well use Score Voting from the start, which is simpler (but has its downsides).