Talk:STAR voting

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References[edit]

For notability, etc.

Omegatron (talk) 14:38, 14 July 2018 (UTC)

I have checked the links. In one case (http://eugeneregisterguard.or.newsmemory.com/publink.php?shareid=2903d8416), I get the following error message: "Sorry, but the shared article you requested doesn't seem to be available." In additional 4 cases (http://www.registerguard.com), I get an "Access Denied" error message. Markus Schulze 10:58, 22 August 2018 (UTC)
The links may have gone invalid, but the articles are still out there and can be found with a cursory web search. For instance, I did the first one (eugeneregisterguard) for you, and archived it at webcitation.org: [1].Homunq () 11:48, 22 August 2018 (UTC)

SRV[edit]

Previous article is here if anything can be salvaged: https://en.wikipedia.org/w/index.php?title=Score_Runoff_Voting&oldid=773896760Omegatron (talk) 15:02, 14 July 2018 (UTC)

Distortion[edit]

The "in order to correct for strategic distortion in ordinary score voting" modified by User:Homunq in https://en.wikipedia.org/w/index.php?title=STAR_voting&diff=850372927&oldid=850296031&diffmode=visual is I think a reference to the distortion caused by normalizing score ballots shown in https://www.youtube.com/watch?v=-4FXLQoLDBAOmegatron (talk) 16:39, 15 July 2018 (UTC)

"Reduce strategic incentives" is clearer, more accurate, and more NPOV. "Correcting" for distortion would imply some correct outcome, which is not well-defined in the current context (and defining it would not be NPOV). Also, I'd say the point of the runoff stage is primarily to reduce the need for strategy in the first place, not to get the right answer in spite of strategy (though those two goals are related). Homunq () 19:09, 15 July 2018 (UTC)

Majority Criterion[edit]

STAR voting doesn't satisfy the majority criterion because it is not guaranteed that a majority winner even gets to the runoff. Markus Schulze 19:35, 18 July 2018 (UTC)

Yeah, only the second round is majoritarian, to discourage strategic exaggeration, but the first round is utilitarian, so it should still behave better than majoritarian systems. Is there a way to say this in NPOV form? I've seen references to "utilitarian welfare criterion", but I think that's a different concept from the normal voting system criteria. — Omegatron (talk) 17:59, 21 July 2018 (UTC)

Reversal Symmetry[edit]

STAR voting doesn't satisfy reversal symmetry.

Example:

Suppose there are three candidates: A, B, C. Suppose candidate A has the best score; candidate B has the second best score; candidate C has the worst score. Candidate B pairwise beats candidate A; candidate C pairwise beats candidate B.
When STAR voting is used, then candidate A and candidate B get into the runoff and candidate B wins.
Suppose the individual ballots are reversed. Then candidate C has the best score; candidate B has the second best score; candidate A has the worst score. Candidate A pairwise beats candidate B; candidate B pairwise beats candidate C.
When STAR voting is applied to the reversed ballots, then candidate C and candidate B get into the runoff and, again, candidate B wins. This is a violation of reversal symmetry. Markus Schulze 19:52, 18 July 2018 (UTC)
Note that this example is only possible if there are exactly 3 candidates. For any other number, there are no violations of reversal symmetry. Homunq () 15:53, 20 August 2018 (UTC)

Participation and Consistency[edit]

STAR voting violates participation and consistency.

Example:

Suppose there are three candidates: A, B, C. Suppose candidate A has the best score; candidate B has the second best score; candidate C has the worst score. Candidate B pairwise beats candidate A; candidate C pairwise beats candidate B.
When STAR voting is used, then candidate A and candidate B get into the runoff and candidate B wins.
Suppose B>C>A ballots are added such that candidate B has the best score, candidate C has the second best score, and candidate A has the worst score, and candidate C still pairwise beats candidate B.
When STAR voting is applied to these ballots, then candidate C and candidate B get into the runoff and candidate C wins. This is a violation of participation and consistency. Markus Schulze 10:42, 22 July 2018 (UTC)

Independence of Clones[edit]

STAR voting violates independence of clones.

Example:

Suppose there are two candidates: A, B. Suppose candidate A has the best score; candidate B has the worst score. Candidate B pairwise beats candidate A.
When STAR voting is used, then candidate A and candidate B get into the runoff and candidate B wins.
Suppose candidate A is replace by clones A1 and A2 such that candidate A1 has the best score, candidate A2 has the second best score, and candidate B has the worst score, candidate A1 pairwise beats candidate A2, candidate B pairwise beats candidate A1, and candidate B pairwise beats candidate A2.
When STAR voting is applied to these ballots, then candidate A1 and candidate A2 get into the runoff and candidate A1 wins. This is a violation of independence of clones (and Condorcet). Markus Schulze 13:10, 22 July 2018 (UTC)

Motivation section[edit]

Motivation

STAR voting is motivated by the idea that adding a ballot and simultaneously adding the inverted ballot should always cancel each other out:<ref>{{Cite web|url=https://www.starvoting.us/equal_vote|title=What is an Equal Vote?|last=|first=|date=|website=|archive-url=|archive-date=|dead-url=|access-date=2018-08-03}}</ref>
"How Do We Know If Our Votes Are Equal? The test of balance is this: Any way I vote, you should be able to vote in an equal and opposite fashion. Our votes should be able to cancel each other’s out."

The Equality Criterion is then defined as follows:<ref>{{Cite web|url=https://www.equal.vote/theequalvote|title=What is an Equal Vote?|last=|first=|date=|website=|archive-url=|archive-date=|dead-url=|access-date=2018-08-03}}</ref>

"A voting method provides votes of equal weight to all the voters if and only if for each possible vote expression that one voter may cast in an election, there exists another expression of the vote that another voter can cast that is in balance - such that the outcome of an election is the same whether both or neither votes are counted.
This test of balance provides the foundation for the Equality Criterion. A voting method passes the Equality Criterion if every possible vote expression has a counter-balancing vote expression and if the counting system produces the same election outcome when any pairing of a vote expression and its counter-balancing vote expression are added to the tally."

Mark Frohnmayer even claims that Arrow's impossibility theorem says that every ranked voting method violates this criterion.<ref>{{Cite web|url=https://www.youtube.com/v/cRPitYNjunA?start=108&end=378&autoplay=1|title=Sex, drugs & the equal vote|last=Frohnmayer|first=Mark|date=|website=|archive-url=|archive-date=|dead-url=|access-date=}}</ref> However, this is a complete misinterpretation of Arrow's theorem. Arrow's theorem is about spoilers (or irrelevant alternatives) and not about the cancellation of votes. Actually, it is easy to see that there are many ranked voting method where adding a ballot and its inverse always cancel each other out. For example, every Condorcet method that uses the margins of the pairwise matrix (e.g. Schulze, ranked pairs, minimax, Kemeny–Young) satisfies this criterion for obvious reasons.

As I said in edit summary, I don't think this kind of writing belongs in a Wikipedia article. Pages like https://www.equal.vote/starvoting https://www.equal.vote/science https://www.equal.vote/report_card https://www.starvoting.us/sightline list a bunch of reasons for why they advocate STAR, but Schulze picks out one of them and claims that it's "their motivation" and then attacks it with his own personal interpretation and no citations. (None of the claims in the Properties section about which ranked-choice voting system criteria it meets have citations, either.) WP:OR and WP:NPOV, etc. — Omegatron (talk) 04:35, 6 August 2018 (UTC)

I don't agree with you. When you read the websites of the STAR voting supporters or when you see the videos of Mark Frohnmayer (the founder of the Equal Vote Coalition), you see that their concept of an "equal vote" is central for their argumentation. (See the definition of the Equality Criterion above.) You can also see that their argumentation is based on a complete misunderstanding of Arrow's impossibility theorem; they mistakenly believe that Arrow's theorem says that it is impossible to create a ranked voting method where adding a ballot and the inverted ballot always cancels each other out. The small number of criteria that are satisfied by STAR voting hardly justifies any advocacy for this method.
Omegatron writes: "None of the claims in the Properties section about which ranked-choice voting system criteria it meets have citations." This talk page contains details on how to construct counterexamples. Markus Schulze 07:06, 6 August 2018 (UTC)
Markus Schulze Our argumentation is not at all based on a misunderstanding of Arrow's theorem. The video you are referencing says that no rank order system can meet the equality criterion because a truncated rank order ballot is impossible to balance. That video then goes on to talk about Arrow's theorem that proved no "fair" rank order system can be made (based on three arbitrary fairness criteria). On watching the video again, I can see how you came to that conclusion, but it's not what is actually said.Nardopolo (talk) 00:48, 15 August 2018 (UTC)
Dear Nardopolo, you wrote: "The video you are referencing says that no rank order system can meet the equality criterion because a truncated rank order ballot is impossible to balance." Your quote shows clearly that Mark Frohnmayer hasn't understood basic concepts of social choice theory. Markus Schulze 18:14, 15 August 2018 (UTC)
Markus Schulze, you wrote "Your quote shows clearly that Mark Frohnmayer hasn't understood basic concepts..." while offering zero supporting evidence. Your notion that the assertion was related to Arrow's theorem as you stated above is not correct. The assertion made in the video and by the Equal Vote Coalition generally is that a rank order ballot that can be truncated cannot be balanced - i.e. if there are 3 candidates A,B,C and one voter ranks only A on the ballot, then there is no way another voter can construct a ranking that would balance that ballot. Recommend you study a little deeper on this one. — Preceding unsigned comment added by Nardopolo (talkcontribs) 19:50, 15 August 2018 (UTC)
Dear Nardopolo, Frohnmayer's TED talk was already discussed in November 2014 at the Election Science mailing list. Already in that discussion, Jameson Quinn wrote: "The upshot is that Frohnmayer is just wrong when he aligns his 'balance' criterion with rated systems or avoiding Arrow." Already in that discussion, I mentioned that those Condorcet methods that are based on margins are a counterexample to Frohnmayer's claims. Markus Schulze 08:46, 16 August 2018 (UTC)
Dear Markus Schulze You are simply reiterating the same misunderstanding of the video you promulgated above. Neither the video nor the Equal Vote site suggest that the balance criterion and Arrow's theorem are at all connected. You also truncated Quinn's statement - his full statement was "The upshot is that Frohnmayer is just wrong when he aligns his 'balance' criterion with rated systems or avoiding Arrow (though he is right about aligning the latter two)." - so Quinn at least partly understood what the video was going for. I clarified this in an email further down the thread you reference: "For the purpose of this talk I assumed no rank order ties and no requirement of complete ballots. I was not trying to give the impression that only rated methods satisfy the equality/balance criterion, but all rated methods do pass the test." Again, your statements above are incorrect, particularly the note that "Your quote shows clearly that Mark Frohnmayer hasn't understood basic concepts of social choice theory." - that notion is not supported by anything you have provided to date. — Preceding unsigned comment added by Nardopolo (talkcontribs) 17:06, 16 August 2018 (UTC)
Dear Nardopolo. Again already in the discussion in 2014, I pointed to the fact that those Condorcet methods that are based on margins are a counterexample to Frohnmayer's claims. Nevertheless he is still speading the false claim that no ranking method can satisfy his Equality Criterion (unless every voter is required to rank every candidate). The same false statements that Frohnmayer made in 2014 can still be found in the current version of his website.<ref>{{Cite web|url=https://www.equal.vote/theequalvote|title=What is an Equal Vote?|last=|first=|date=|website=|archive-url=|archive-date=|dead-url=|access-date=2018-08-03}}</ref> Markus Schulze 17:57, 16 August 2018 (UTC)
Dear Markus Schulze you did not point out then, nor do you point out now, how margin based Condorcet methods are a counterexample to the Equal Vote claims; you merely asserted it. The balance criterion says that for every vote expression there must exist a counterbalancing vote expression such that the result of the election is the same if both or neither are counted. If you have a proof that there are rank order methods that satisfy this criterion, even in the presence of truncated ballots, then we will adjust the Equal Vote pages to match. — Preceding unsigned comment added by Nardopolo (talkcontribs) 21:54, 16 August 2018 (UTC)
Dear Nardopolo, suppose N[X,Y] is the number of voters who strictly prefer candidate X to candidate Y.
Step1:
Case 1: Suppose on the original ballot, candidate A is strictly preferred to candidate B. Then on the inverted ballot, candidate B is strictly preferred to candidate A. So the original ballot increases N[A,B] by 1 and keeps N[B,A] unchanged and the inverted ballot increases N[B,A] by 1 and keeps N[A,B] unchanged.
Case 2: Suppose on the original ballot, candidate B is strictly preferred to candidate A. Then on the inverted ballot, candidate A is strictly preferred to candidate B. So the original ballot increases N[B,A] by 1 and keeps N[A,B] unchanged and the inverted ballot increases N[A,B] by 1 and keeps N[B,A] unchanged.
Case 3: Suppose the original ballot is indifferent between candidate A and candidate B. Then also the inverted ballot is indifferent between candidate A and candidate B. So the original ballot keeps N[A,B] unchanged and N[B,A] unchanged and the inverted ballot keeps N[A,B] unchanged and N[B,A] unchanged.
So adding a ballot and the inverted ballot never changes the margin N[A,B]-N[B,A] of the pairwise matrix.
Step2:
To see that for every ballot there is an inverted ballot, you only have to prove that, when ">" is a strict weak ordering, then also "<" is a strict weak ordering. So you have to prove that, when ">" is irreflexive, asymmetric, transitive, and negatively transitive, then also "<" is irreflexive, asymmetric, transitive, and negatively transitive. To do this, you only have to rename the candidates and to use the fact that X>Y if and only if Y<X.
For example, the fact that ">" is transitive means:
(1) If A>B and B>C, then also A>C.
To prove that "<" is transitive, you have to prove:
(2) If A<B and B<C, then also A<C.
But you get (2) from (1) simply by renaming candidate A and candidate C and by using the fact that X>Y if and only if Y<X.
In short: For every possible ballot, there is an inverted ballot. And adding a ballot and the inverted ballot never changes the margins of the pairwise matrix. Markus Schulze 07:09, 17 August 2018 (UTC)
Dear Markus Schulze It appears your example requires the ability for the voter to express equality of ranking, no? I.e. not just A>B>C but A=B>C. The email on the election science list clarified that the video assumed no equalities of ranking were allowed on the ballot and that the voter is allowed to truncate. This is a good clarification to make on the Equal Vote site. It comes from the fact that ranked methods used in the U.S. allow (and most times force) truncation, and do not allow equality of ranks. If I misinterpreted your proof, feel free to clarify in lay terms that can be published to a wider audience. — Preceding unsigned comment added by Nardopolo (talkcontribs) 04:10, 20 August 2018 (UTC)
It appears that the Equal Vote definition page has been updated to clarify what is written above: https://www.equal.vote/theequalvote -- does it now make sense? Nardopolo (talk) 07:30, 20 August 2018 (UTC)

(de-indent) This debate includes Markus Schulze, nardopolo, citations of Mark Frohnemayer and Jameson Quinn, and now homunq (me) — but I have reason to believe that this is fewer than 5 different people. While Markus Schulze is correct that "balance" in Frohnemayer's sense can be satisfied by strictly ranked voting methods, nardopolo and Frohnemayer are correct that it cannot be satisfied by voting methods that allow truncation but otherwise require strict rankings. It appears to me, therefore, that Schulze is misconstruing the arguments of the other voices present here. I'm certain that Schulze is intelligent enough not to so misconstrue if he did not want to.

However, the relevant section is no longer on the page, so I believe this is moot. Homunq () 11:48, 20 August 2018 (UTC)

Monotonicity[edit]

Suppose STAR voting is used. Suppose candidate B wins.

Suppose a single ballot with A="5", B="4", C="3", D="2", E="1", F="0" is replaced by a ballot with B="5", A="4", C="3", D="2", E="1", F="0". Suppose candidate C is the new winner. This can happen e.g. when, in the original situation, candidate A and candidate B got into the runoff and candidate B pairwise beat candidate A and, in the new situation, candidate B and candidate C get into the runoff and candidate C pairwise beats candidate B.

Now does this example show a violation of the monotonicity criterion? It shows a violation of the monotonicity criterion in the sense that is usually used for ranked voting methods. It doesn't show a violation of the monotonicity criterion in the sense that is usually used for cardinal voting methods. This is explained in great detail at the website by Warren D. Smith.<ref>{{Cite news|url=https://rangevoting.org/StarVoting.html|title=STAR voting|last=|first=|date=|work=The Center for Range Voting|access-date=2018-08-03|quote=STAR elections can be nonmonotonic with a slightly wider sense of the word.}}</ref> Markus Schulze 18:11, 15 August 2018 (UTC)

By the way: When score voting is used, then replacing a ballot A="5", B="4", C="3", D="2", E="1", F="0" by a ballot B="5", A="4", C="3", D="2", E="1", F="0" cannot change the winner from candidate B to candidate C. Markus Schulze 04:21, 16 August 2018 (UTC)
Dear Markus Schulze, your example is not, in any way, an example of a violation of the monotonicity criterion. Both your example and the one on Smith's page rely on changing the score of two candidates on the ballot. Yet the several definitions of the monotonicity criterion that appear consistent and widely accepted in the social choice world read as follows:
1. On Wikipedia - "The monotonicity criterion is a voting system criterion used to evaluate both single and multiple winner ranked voting systems. A ranked voting system is monotonic if it is neither possible to prevent the election of a candidate by ranking them higher on some of the ballots, nor possible to elect an otherwise unelected candidate by ranking them lower on some of the ballots (while nothing else is altered on any ballot). [1] In single winner elections that is to say no winner is harmed by up-ranking and no loser can win by down-ranking." (ed. as you pointed out in a roundabout way above, a true ranking is A > B, A = B, A < B. In ranking as in rating, it is possible to increase support for A without decreasing support for B, even though many of today's contemporary rank-order systems do not allow equality of ranks on the ballot.)
2. From Center for Election Science: "Monotonicity is an election method criterion that requires the following: Ranking or rating a candidate higher should never cause that candidate to lose, nor should ranking or rating a candidate lower ever cause that candidate to win, assuming all other candidates remain rated or ranked the same. In other words, an election method is non-monotonic if either of the following is possible: A winner can be changed to a loser by experiencing an increase in support, OR A loser can be changed to a winner by experiencing a decrease in support." (ed. CES introduces the notion that the monotonicity criterion can be applied to rank order as well as rated systems.)
3. From Rangevoting.org, Smith's own site: "Monotonicity is the property of a voting system that both: If somebody increases their vote for candidate C (leaving the rest of their vote unchanged) that should not worsen C's chances of winning the election [and] If somebody decreases their vote for candidate B (leaving the rest of their vote unchanged) that should not improve B's chances of winning the election." [see https://rangevoting.org/Monotone.html]
4. From Lynn Arthur Steen, professor of mathematics at St. Olaf College, Northfield, Minnesota: "With the relative order or rating of the other candidates unchanged, voting a candidate higher should never cause the candidate to lose, nor should voting a candidate lower ever cause the candidate to win." [from Clay Shentrup: In other words, an election method is non-monotonic if either of the following is possible: A can be changed to a loser by experiencing an increase in support ("mono-raise"), [and] A loser can be changed to a winner by experiencing a decrease in support ("mono-lower")]
There is a consistent theme in the above, namely that monotonicity, and VERY specifically the "monotonicity criterion" refer to increasing or decreasing support for one candidate while leaving the rest of the vote unchanged. The example given by Warren Smith that Markus Schulze has pasted here includes increasing support for a candidate AND decreasing support for another. A recent post on the Center for Election Science mailing list from expert Jameson Quinn to Smith summarizes this crisply:
"You're right; [labeling STAR non-monotonic] wasn't an error. It was an attempt to redefine monotonicity to something you think is more important. You may or may not be right, but I still think that "monotonicity" should not be the word for your new concept. STAR is monotonic."
Smith at least is honest with his words when he clarifies that he is talking about monotonicity "with a slightly wider sense of the word." He is not directly trying to change a well-established voting method criterion. That's an out that your statement above is not afforded, because your edits refer directly to the monotonicity criterion itself. Perhaps it is Schulze who doesn't understand "basic concepts of social choice theory"? Nardopolo (talk) 06:56, 20 August 2018 (UTC)
I don't question that STAR voting satisfies the monotonicity criterion in the sense that is usually used for cardinal voting methods. However, STAR voting doesn't satisfy the monotonicity criterion in the sense that is usually used for ranked voting methods: "A ranked voting system is monotonic if it is neither possible to prevent the election of a candidate by ranking them higher on some of the ballots, nor possible to elect an otherwise unelected candidate by ranking them lower on some of the ballots (while nothing else is altered on any ballot)." Markus Schulze 07:54, 20 August 2018 (UTC)
Dear Markus Schulze Your statement is false. Your scenario requires de-ranking a second candidate (whether in a cardinal or rank-order sense). The section you've added to the page relies entirely on Smith's admittedly "biased" and "PRELIMINARY" analysis, and thus does not IN ANY WAY constitute a valid source here on Wikipedia. Please stop changing my edits until you have a valid source. Nardopolo (talk) 08:11, 20 August 2018 (UTC)
When we talked about a ranked voting method, it would be considered a violation of monotonicity when changing a ballot from A="5", B="4", C="3", D="2", E="1", F="0" to B="5", A="4", C="3", D="2", E="1", F="0" changes the winner from candidate B to candidate C. Markus Schulze 10:20, 20 August 2018 (UTC)


(de-indented) OK, there is now clear evidence of edit warring on both sides. First, I'm going to discuss the definition of the Monotonicity criterion. That article equates the term to what Woodall termed "mono-raise" in [2]. STAR very clearly does not violate this criterion, and Markus Schulze's example above is not germane.

Woodall himself gives 7 different monotonicity criteria, of which mono-raise is only the first. Of those, STAR passes only mono-raise. I've seen other more-complete lists of monotonicity criteria which include other ones that Woodall missed and STAR passes, such as mono-add-plump (which does not imply and is not implied by mono-raise).

Is mono-raise the canonical monotonicity criterion, as the relevant wikipedia article currently states? Let's look at the other, more recent references cited by that article:

  • [3] ... this considers only strictly ordinal rules; by the definition there, STAR is not even a voting method. Does not directly apply. However, within the limits of this constraint, the given definition of "monotonicity" is equivalent to mono-raise.
  • [4] Ditto.
  • [5] In formal terms, this has the same problem as the two articles above; it considers only fully-ranked voting methods. However, it does include the following less-formal (English) definition of monotonicity: "An election profile P exhibits an upward monotonicity failure if there exists a profile P� that is identical to P except that candidate A [the winner under P] is ranked higher by a subset of voters, but candidate A is not the IRV winner." Schulze is in essence arguing that the word "ranked" in this definition is absolutely key even for rated voting methods; Nardopolo is in essence arguing that this word should be replaced by "rated" when discussing rated methods. Since this definition is equivalent to mono-raise for ranked methods, I think it's evidence that unqualified "monotonicity" is generally understood to mean mono-raise; in other words, I think this should count as evidence in Nardopolo's favor.
  • [6] This article gives only the following incomplete definition of monotonicity: "...a condition known as non-monotonicity. This has a complex definition, but is most easily explained as a condition where a candidate can increase their chances of victory by lowering their first preference count." It's clear that Antony Green does not consider this the only meaning of monotonicity, but it's also clear that STAR passes by this definition.

So all in all, I'd say that "monotonicity" is generally understood as "mono-raise", which STAR passes. Homunq () 11:22, 20 August 2018 (UTC)

I decided to take this further; I searched "monotonicity voting cardinal" on Google Scholar and clicked on the 6 links in the first page of results that appeared potentially relevant. These include: (sorry, Harvard proxy in urls)
  • [7] Discusses how ordinal voting methods work for cardinal agents. Does not define "monotonic" for cardinal voting methods.
  • [8] Doesn't mention monotonicity, don't know why it came up. (Also, a whole paper on voting dedicated to proving Pareto dominance is Unclear On The Concept. The class of situations where Pareto dominance applies has no overlap with realistic voting scenarios.)
  • [9] Doesn't actually mention cardinal voting methods; unrelated use of "cardinal".
  • [10] Uses cardinal mono-raise as the primary definition of monotonicity, though other definitions are discussed.
  • [11] Defines monotonicity for ordinal methods and for approval voting. Both definitions are special cases of cardinal mono-raise.
  • [12] Doesn't define monotonicity (only reference to it is a citation of one of Schulze's papers).
So, though I still don't have a slam-dunk proof that cardinal mono-raise is the best definition of "monotonic" to use here, I think this evidence further tends to support that proposition. In particular, the definition of monotonicity for approval voting is a clear counterexample to Schulze's argument that only the ordinal definition is accepted. Homunq () 14:46, 20 August 2018 (UTC)

Resolvability criterion[edit]

Tideman's version:

Say there's a result which incļudes ties for top score, ties for second-top score, and all candidates in those ties are also tied pairwise. If X and Y are any two candidates tied for top score, then a ballot which gives X 5 points, Y 4, and all other candidates 0 points will ensure X wins in STAR. Thus STAR is resolvable in Tideman's sense.

Woodall's version:

As the number of voters tends towards infinity, each candidate's overall score tends to a normal distribution, by the Central Limit Theorem. This is a continuous distribution, thus under it, exact ties for score have probability zero. (Formalizing this argument would be tedious, and would not actually rely on the continuity of the normal, but merely on the fact that the probability of any specific score approaches zero.) Meanwhile, the probability of exact pairwise ties in the runoff is zero as voter number goes to infinity, because it's well-known that pairwise plurality elections are Woodall-resolvable. (Can argue based on the probability of an exact 0 for a standard normal under the CLT, as above.)

Homunq () 12:17, 20 August 2018 (UTC)

Ratings to rankings problem among many candidates[edit]

The failure of this method seems to be the use of a single ballot for both rounds. Say there are 5 Democrats running, and there's a chance two of them will make it to the second round, then all 5 ratings are needed to distinguish them. However if ALL Democrats rank 5 candidates uniquely for use in the second round, the average rating for Democrat candidates will be 3=(1+2+3+4+5)/5. Meanwhile if 2 Republicans run they can be ranked with an average score of 4.5=(4+5)/2. So if 55% of voters vote for all Democrats, and 45% Republicans, the average Democrat score will be 55%*3=1.65 score, and the average Republican will get 45%*4.5=2.025 score, and its possible both Republicans will make top-2, even better chances if Republicans vote 5 on both. So the 55% majority Democrats will have no vote in round 2 just because they wanted to rank them. And WORSE, if they have a preference among the Republicans, giving that preference further threatens to help that Republican defeat the Democrats from making top-2! Tom Ruen (talk) 02:21, 10 December 2018 (UTC)

A more acceptable solution would have a hierarchical vote, so I can vote 5.5 for my favorite and 5.4,5.3,5.2,5.1 for my best alternatives, while all scored as 5 votes. And I could also vote 0.5,0.4,0.3,0.2,0.1 for my evaluation of the rivals I don't want, getting 0 ratings in the first round but a preference in the second round if I must choose. Tom Ruen (talk) 02:34, 10 December 2018 (UTC)
I see a tactic that would maximize a chance of winning would be: (1) Rate 5 for all acceptable candidates. (2) Rate 4 for extreme candidates who have a chance to eliminate more centrist rivals (3) Rate 0 on dangerous rivals. Ideally TWO acceptable candidates make top-2, but if only one of them makes it, you'll give a full vote for that candidate, and if you happened to give a 4 score to your final rival, that insincere vote will evaporate, while still helping to eliminate a stronger rival in the first round. The only danger is if no acceptable candidates make the runoff, and then you'd be helping an extreme candidate. For example a Republican might vote Republican=5, Libertarian=5, Socialist=4, Democrat=0. If the Democrat and Socialist win, they're equally bad, but if the extreme socialist wins, the Republicans will have a stronger case against a weaker incumbent next time. Tom Ruen (talk) 13:20, 10 December 2018 (UTC)

FairVote report and non-NPOV section[edit]

Someone had added a badly-non-neutral "criticism" section near the front. I trimmed it and moved it to a more balanced discussion section near the end. I think it's OK as it now stands, but the FairVote essay that was the main citation of that section is very borderline as a reliable source, so I'd strongly object to restoring the bits I trimmed. Homunq () 01:35, 18 June 2019 (UTC) This section has been further adjusted to include an analysis of the FairVote citation from STAR advocates.Nardopolo (talk) 23:01, 7 July 2019 (UTC)