Talk:Ranked voting: Difference between revisions
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::::::: This is not a very important point, so first off, you are free to skip the discussion on it. But I just want to try to clarify it if possible. So, as an example, let's say a voter maximally prefers A to B. On a rated ballot, it is clear as to how they should express this: put A at the max score and B at the min score. But now let's say they also prefer B to C to some extent. This preference can't be mentioned on a rated ballot, since there is no further room for differentiation when you put the more-preferred candidate at the min score. I am mentioning the idea of cardinal pairwise matchups because it'd allow you to do this, and am further pointing out that a ranked ballot is really equivalent to always putting your more-preferred candidate at the max score and the less-preferred candidate at the min score in each matchup. Thus, this seems a better way to categorize rated and ranked ballots to me than to say that ranked is a subcategory of rated; a ranked ballot doesn't prevent the voter in my example from voting both A>B and B>C while having maximally strong preferences in both matchups. To be clear, this isn't an argument for "ranked ballots are better than rated ballots", but just pointing out that they both capture certain pieces of information that would be lost by converting to the other i.e. a Bernie>Biden>Trump voter with strong preferences between all 3 may not be able to honestly score Biden in between Bernie and Trump without weakening at least one of the matchups, and likewise, ranked ballots can't detect if you only slightly prefer A to B. The generalized cardinal pairwise approach allows one to express both weak preferences in some matchups, and strong preferences in others, so that is why I'm saying it's a useful theoretical concept to help unify rated and ranked ballots conceptually. It is not practical of course to have a voter fill out each and every matchup, but approximations can be done, such as allowing a voter to rate the candidates and then say if they want the weak preferences to be processed, or for each preference to be treated as maximally strong. This is why I mentioned Score being a subset of Condorcet: if you give A 100% support, B 80%, and C 0% on a rated ballot, that is equal to giving 0.2 votes to A>B and 0.8 votes B>C in a Condorcet method. If these preferences are treated as ranked, though, then it is equivalent to giving 1 vote in each matchup to the more-preferred candidate. Sorry for the lengthy response. Edit: It may help to point you to academic articles on this; I don't really understand them well, but I believe the generalized cardinal pairwise preferences I'm speaking about are called "fuzzy pairwise comparisons" in the academic literature. For example, (PDF) https://tarjomefa.com/wp-content/uploads/2015/06/3073-engilish.pdf. Again, I don't understand it all, but I think it gives you a rough idea of what I'm talking about. [[User:BetterVotingAdvocacy|BetterVotingAdvocacy]] ([[User talk:BetterVotingAdvocacy|talk]]) 03:30, 14 April 2020 (UTC)
I would strongly advise us to remove this bit. It's confusing and mostly incorrect. Cardinal ballots are fundamentally different from ranked ballots, and interval scales are not the same thing as a ranking. Mathematically, cardinal ballots contain more information than ranked ballots and cannot be treated as subsets: the opposite is mathematically true ''under the assumption of transitivity''. [[User:BetterVotingAdvocacy|BetterVotingAdvocacy]] is correct when they state both are subsets of a more general type of ballot which does pairwise comparisons. One can see cardinal ballots as marginals of such pairwise rating ballots, and ordinal ballots as a further discarding of information from cardinal ballots (again, if you assume transitivity). [[User:lucasvb|lucasvb]] ([[User_talk:lucasvb|talk]]} 14:14, 19 July 2020 (UTC)
: I agree that both ranked and Score ballots are subsets of the [[rated pairwise preference ballot]]. But further, an argument can be made that a Score ballot is equivalent to multiple fractional ranked ballots, though I don't have an issue with removing the piece you're against. Consider that a Score ballot A:5 B:4 C:3, on a scale of 0 to 5, is equivalent to 0.6 ABC Approval ballots (i.e. a Score ballot of A:3 B:3 C:3), 0.2 AB ballots, and 0.2 A ballots (see [[KP transform]]). And obviously, Approval ballots are ranked ballots where the approved candidates are ranked 1st, and the other candidates ranked last. So in some sense, ranked ballots really are a superset of Score ballots, when we make room for fractional ballots. [[User:BetterVotingAdvocacy|BetterVotingAdvocacy]] ([[User talk:BetterVotingAdvocacy|talk]]) 16:00, 19 July 2020 (UTC)
== Conflation of ballot type and tabulation type ==
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: His arguments can be found in more length at https://www.reddit.com/r/EndFPTP/comments/hi29r8/discussion_of_a_vote_form_an_score_example/fweu53r/ and https://www.reddit.com/r/EndFPTP/comments/hi29r8/discussion_of_a_vote_form_an_score_example/fwey9w4/. [[User:BetterVotingAdvocacy|BetterVotingAdvocacy]] ([[User talk:BetterVotingAdvocacy|talk]]) 18:23, 8 July 2020 (UTC)
:: I did not see a discussion of the relation of Majoritarianism to Utilitarianism. --[[User:Dr. Edmonds|Dr. Edmonds]] ([[User talk:Dr. Edmonds|talk]]) 03:50, 9 July 2020 (UTC)
::: In the second comment, he says "So, you are assuming "1 unit of potential violence" for every person equally, assuming you can aggregate those units, then assuming the side with "more violent potential" wins.
::: You are assuming the power to be violent and the amount of violence inherent in each person is equal and commensurable, and aggregating it."
::: This is what you were saying with majority rule being a "first order approximation" of utilitarianism. [[User:BetterVotingAdvocacy|BetterVotingAdvocacy]] ([[User talk:BetterVotingAdvocacy|talk]]) 04:45, 9 July 2020 (UTC)
: I think that you misunderstood things. The argument here is about ordinal vs cardinal utilities, not majoritarianism vs utilitarianism, and I'm certainly NOT claiming the Pareto equilibrium is utilitarian (which is incorrect, as the dicator example clearly demonstrates), only pointing out that the Paretian ideas are present in the economics literature.
: The point is that under strictly ordinal preferences (if you are working ONLY within an ordinal utility framework, like economists do), arbitrarily anti-democratic situations must be considered acceptable, as Pareto equilibrium (the best you can do under such framework) implies you cannot violate the preferences of even a single individual, like the dictator, when changing social states. Every change has to be unanimously positive or neutral.
: This shouldn't be controversial, as it's all pretty standard in the ordinal vs cardinal utility literature.
: This argument is usually presented inverted in the literature (typically right-wing Libertarian), when people use Paretian principles to criticize democracy as a form of social organization and promote free market principles as an alternative: "democracy is two wolves and a sheep deciding what's for dinner", they say. To prevent the "mob rule" from violating even a single individual's rights, one invokes Pareto equilibrium: the wolves cannot get what they want without violating the preferences of the one sheep, so if you claim to defend individual rights absolutely you need every single individual to either agree or be indifferent to a change in the social state. Since the sheep doesn't want to get eaten, society just lives with the status quo and the sheep lives. This is seen as a triumph of "free-market" (but in actuality Paretian) principles over "mob rule" (democracy).
: This is precisely the same argument I've outlined, but now the sheep (dictator) is the villain of the story. If you wish to change to a different social state, you necessarily must violate the preferences the dictator has to remain in power. You also need an additional justification outside your framework to do so. So a Paretian framework necessarily invalidates any move towards the will of the majority, or any sense of democracy. To navigate the Pareto frontier towards a "better outcome" one must invoke some additional principles.
: The only solution out of this is to invoke some notion of CARDINAL utilitarianism, by claiming that every individual has equal claim to violate anyone else's will (I referred to "violence" in those reddit posts as that was the argument being used), and so the largest group thus decides which minority preferences to violate in their favor. This is majority rule, but it is fundamentally a cardinal utilitarian argument as you necessarily must aggregate multiple individuals preferences in a cardinal way. Under strictly ordinal preferences, there is no such concept as "counting"!
: Another point that seems wasn't clear is that cardinal utilities doesn't mean "non-uniform strength of preferences". If everyone is assumed to have exactly the same utility and you add them up, you're still operating under a cardinal utilitarian framework, you're still "adding multiple individuals".
: The claim that my A>B cancels your B>A ("every individual has equal claim to violate anyone else's will") is a cardinal claim, and this is underlying majority rule. You are simply assuming every ordinal preference has exactly the same cardinal utility difference when comparing them. Perhaps this can be edited to make the argument cleare, and I could fetch some references for specific points later on. [[User:lucasvb|lucasvb]] ([[User_talk:lucasvb|talk]]} 17:43, 18 July 2020 (UTC)
:: [[User:Lucasvb]] This is the first I am hearing of '''ordinal utilities'''. I do not see how this term is useful. Utilities are generally thought of as a numeric measure. Ordinal systems only provide a preference direction not a magnitude. this term conflates preference with Utility. Is this term used in literature anywhere? I think you just mean preference when you say ordinal utility. If that is the case then why not use the less confusing term? --[[User:Dr. Edmonds|Dr. Edmonds]] ([[User talk:Dr. Edmonds|talk]]) 21:22, 18 July 2020 (UTC)
:::: That's surprising, as it's THE standard term used everywhere, and it's even already mentioned in the article's reference section. https://en.wikipedia.org/wiki/Ordinal_utility or https://scholar.google.com/scholar?hl=en&as_sdt=0,5&q=ordinal+utility ... Utilities are what individuals use to make decisions. I don't like the term either, but since it exists we cannot use "utility" without clarification. [[User:lucasvb|lucasvb]] ([[User_talk:lucasvb|talk]]} 09:33, 19 July 2020 (UTC)
::::: Thanks for the links. It seems you are right. --[[User:Dr. Edmonds|Dr. Edmonds]] ([[User talk:Dr. Edmonds|talk]]) 18:21, 19 July 2020 (UTC)
:: I disagree. To me, the claim that ordinal voting is really cardinal feels like the (obvious) observation that any ethics system can be cast as a form of utilitarianism, because every ethics system cares about some values and disregards others. For instance, you can make deontology utilitarian by saying that the adherents assign utility -infinity to going against their duty; or you can make Rawlsian justice utilitarian by considering it a variant of minmax utilitarianism. However, neither deontology nor Rawlsian justice are, to my knowledge, usually considered to be utilitarian.
:: So what's the logic of (majoritarian) ordinal voting? Well, it's these two things:
::: 1. Each person's voice is of equal value (this can be justified by some kind of veil of ignorance or birth lottery argument without importing the whole machinery of total utilitarianism).
::: 2. Beyond that, we don't know what the voters' relative scales are (e.g. if A>B does that mean A: 1000, B: 1, or A: 10, B: 1?), and we have no basis for interpersonal comparison (is my first preference stronger than yours?).
:: There are other variants of ordinal voting that are not majoritarian, and thus discards the first point here. For instance, the Heitzig consensus scheme I've been talking about recently on the EM list is closer to the Rawlsian approach, although it isn't quite the same thing. While the scheme is not majoritarian, I'd still consider the voting done in it ordinal, however. [[User:Kristomun|Kristomun]] ([[User talk:Kristomun|talk]]) 09:45, 21 July 2020 (UTC)
:: Thinking about this a bit more, I suppose all ordinal methods are, in the sense that say Plurality or Borda is, cardinal, because their algorithms use numeric variables. But by that criterion, every deterministic, neutral, anonymous, and resolvable voting method is "cardinal". What the argument above shows is that ordinal methods are not necessarily utilitarian, or approximately utilitarian, unless every system of ethics that can be cast in a utilitarian form is also utilitarian. [[User:Kristomun|Kristomun]] ([[User talk:Kristomun|talk]]) 11:18, 21 July 2020 (UTC)
::: [[User:Kristomun|Kristomun]] That is well put. I think electowiki needs a page on this topic. A sort of comparison between the majoritarian and utilitarian philosophies which underpin different systems. I tried to give an explanation of a specific point of that [https://forum.electionscience.org/t/utilitarian-vs-majoritarian-in-single-winner/602 here]. Are you interested in giving it a shot. I have always been hesitant because I do not know where to start.
::: On a different topic are there any Rawlsian minmax electoral systems? I tried to use the total number of unspent points as a metric in PR systems to measure quality. ie MAX-sum(score) for each voter is the amount of unspent score. So you want to try to minimize the total amount of unspent score. This is basically what [[Sequentially Spent Score]] does with its reweighting but the selection is pure Utilitarian. --[[User:Dr. Edmonds|Dr. Edmonds]] ([[User talk:Dr. Edmonds|talk]]) 15:42, 21 July 2020 (UTC)
:::: There are the so-called "consensus" or "minmax" multiwinner methods, like [[Minimax approval]]. Let a voter's satisfaction with a council be his max score of a candidates on that council. Then minmax Range chooses the council so as to maximize the minimal satisfaction with that council. Approval is easier, it just minimizes the maximal Hamming distance. Since min and max are not robust statistics, these methods are vulnerable to strategy.
:::: In addition, I'd say unanimity-based voting would fit, because if the worst-off voter doesn't agree to the proposal, it doesn't happen. However, high supermajority and unanimity voting have a status-quo bias, which is what the Heitzig mechanism I've referred to tries to do away with.
:::: As for your other question, I might, but I think I would need more time than I have at the moment to just sit down and think about, as you put it, where to start. So perhaps someday! [[User:Kristomun|Kristomun]] ([[User talk:Kristomun|talk]]) 17:00, 21 July 2020 (UTC)
::::: [[User:Dr. Edmonds|Dr. Edmonds]], I've written a very rough first version here: [[User:Kristomun/Voting_system_philosophies]]. [[User:Kristomun|Kristomun]] ([[User talk:Kristomun|talk]]) 11:41, 16 October 2020 (UTC)
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