Okay, Ned, thank you for writing this. Specifically:
"The ballot in an Instant Bracket Voting election could look the same as ballots in any Ranked-Choice Voting election. The voters would rank the candidates in order of preference, ..."
We must make it clear that, in this case, this *is* a form of Ranked-Choice Voting and not allow FairVote to appropriate the umbrella term to mean only Instant-Runoff Voting. Personally, I think that's the *only* way Instant Bracket Voting can be done. Expecting voters who never ever think about March Madness or athletic tournaments to fill out brackets on their ballot is not going to fly. Not in my opinion. It has to be a ranked-ballot, RCV. (But not IRV.)
But then the question I have is this: We know that this is Condorcet-consistent, so we know that no matter how it's seeded, if there is a Condorcet winner (which is 99% of the time) that Condorcet winner will be elected. But if there is *no* Condorcet winner, the outcome of the election will depend on how the first round is seeded. That's a problem. The method should be deterministic and not depend at all on a random manner of who gets matched up with whom.
That's why I think that Round Robin (or what I might call "straight-ahead Condorcet") is fairer and clearer than Instant Bracket Voting. And if there *is* a cycle, it's not exactly a tie unless the votes were perfectly symmetrical between the candidates involved in the cycle (the Smith set).
Consider a Round-Robin Tournament that ends up lacking a Condorcet winner. If it were hockey or basketball or wrestling, they could do as Nic Tideman suggests and favor the matches with scores having wider margins over the matches with smaller margins as a basis for identifying the champion. Or Minimax.
The BTR-IRV was attractive because it is the smallest modification to Hare IRV that makes IRV Condorcet-consistent and the modification is easily understood, It's also a Single-method Condorcet system. It just does what it does and someone is elected. If there is a Condorcet winner, that candidate will be elected. If there isn't, someone is still elected with this single method.
The reason we settled on a Two-method Condorcet system was because this legislator, the legislative counsel, and I all agreed that "The law should say what it means and mean what it says."
It seemed that straight-ahead Round Robin, with language to meaningfully resolve a cycle, would be easiest for everyone to understand and to buy into it. If there ever was a cycle, most people would accept the resolution of the cycle as fair. If I were to do it again (and we might do it again this session, I dunno), I think it would be Condorcet-TTR for top-two runoff instead of Condorcet-Plurality. That would make it elect the Hare IRV winner in the case of a cycle involving just the top three candidates.
But I'm a little nervous about this Instant Bracket Voting if there is a Condorcet cycle and the outcome depends on how the candidates are seeded. It shouldn't.
Interesting idea. I’m concerned that bracket voting is heavily sensitive to how the brackets are constructed: at least in cases where there’s no clear Condorcet winner, different algorithms for constructing the brackets could produce different winners, so whoever controls those algorithms has an opportunity to control the election.
You compare instant bracket voting with instant runoff voting, of which I’m a lukewarm fan. How does instant bracket voting compare to Borda-count ranked voting (which is also relatively easy to explain)? IIRC, Borda almost always picks the Condorcet winner where there is one, but needs no tie-breaking mechanism; more importantly, there’s no separate “build the brackets” step providing opportunities for manipulation.
The rare cases where Borda disagrees with Condorcet are because Condorcet asks which of two candidates each voter prefers, but ignores the additional information of _how strongly_ they prefer one over another; it treats the head-to-head comparison of a 4th-ranked and a 5th-ranked candidate the same as the comparison of a 1st-ranked and a 10th-ranked candidate. Suppose 49% of voters rank Bob in last place (in a field of three or more) and Chris first, while 51% rank Bob first and Chris second. Bob is the Condorcet winner, but Borda, using more information, picks Chris.
The sports analogy is exactly why I think people might distrust this system. I suspect that Condorcet cycles are more common in sports than in politics: I can easily see Team A having strengths that enable it to beat Team B, which has strengths that enable it to beat Team C, which has strengths that enable it to beat Team A. And I can easily see fans of team A feeling cheated that team C was matched first against A rather than B.
Also, I don’t take it as axiomatic that electing the Condorcet winner where one exists is always right; see the last paragraph of my previous comment.
But if you do accept the Condorcet criterion, then precisely because Condorcet cycles are rare, it doesn’t matter much how you pick the Condorcet winner; there’s no particular advantage to brackets over counting wins in a round-robin tournament.
> "But if you do accept the Condorcet criterion, then precisely because Condorcet cycles are rare, it doesn’t matter much how you pick the Condorcet winner; there’s no particular advantage to brackets over counting wins in a round-robin tournament."
I'm in general agreement, being a Condorcet advocate.
Cycles are rare. Appear to be less than 1% (2 RCV elections in the US so far have been a Rock-Paper-Scissors cycle. 2 other RCV elections had a Condorcet winner but IRV failed to elect the CW.)
It's most important to *get* RCV reformed to be Condorcet-consistent than worrying about which Condorcet method. Hard core geeks seem to like Schulze the best. I like Ranked-Pairs. But I was able to get my legislator to introduce a Condorcet RCV bill and then it appeared that, given the initial suspicion of RCV and a "new RCV", that then it was important for the law to simply say what it means and mean what it says. That meant a two-method system where the simple round-robin pairwise contest intended to identify the one candidate who never loses to anyone. And in the case that no such Condorcet winner exists, then a simple, straight rule perceived to be fair (like Plurality or Top-Two Runoff) is used. Then the intent of the law is most apparent from the legislated language.
> "The rare cases where Borda disagrees with Condorcet are because Condorcet asks which of two candidates each voter prefers, but ignores the additional information of _how strongly_ they prefer one over another; ..."
Condorcet pointed out that voters will strategically exaggerate the relative strength in preference to increase the odds for their candidate. Borda is inherently vulnerable to strategic Burying, as is Score Voting or any cardinal system (even Approval Voting).
Borda's defense was "My system is only intended for honest men." That is weak. We need the system to be invulnerable (as much as possible) to nefarious or strategic actions of dishonest persons. We don't want the system to be gamed.
> "... it treats the head-to-head comparison of a 4th-ranked and a 5th-ranked candidate the same as the comparison of a 1st-ranked and a 10th-ranked candidate. "
As it should. “One person, one vote” mean that every enfranchised voter has an equal influence on government in elections because of our inherent equality as citizens and this is independent of any utilitarian notion of personal investment in the outcome.
If I enthusiastically prefer Candidate A and you prefer Candidate B only tepidly, your vote for Candidate B should count no less (nor more) than my vote for A. The effectiveness of one’s vote – how much their vote counts – is not proportional to their degree of preference but is determined only by their franchise. A citizen with franchise has a vote that counts equally as much as any other citizen with franchise.
For any ranked ballot, this means that if Candidate A is ranked higher than Candidate B then that is a vote for A, if only candidates A and B are contending (such as in the RCV final round). It doesn’t matter how many levels A is ranked higher than B, it counts as exactly one vote for A.
"Condorcet pointed out that voters will strategically exaggerate the relative strength in preference to increase the odds for their candidate. Borda is inherently vulnerable to strategic Burying, as is Score Voting or any cardinal system (even Approval Voting)."
Yes, there are scenarios in which Borda rewards insincere voting, and you're quite right that appealing to "honest men" is a feeble argument. But those scenarios are rare, and they depend on knowing with some precision how everybody else is going to vote. If you don't know how everybody else is going to vote (especially difficult if they might vote insincerely too!), Borda tends to punish insincere voting in the most appropriate way: by giving you what you said you wanted. If you sincerely feel A > B > C > D but vote A > C > D > B to boost A's chances, and A turns out to have less support than you estimated, you may end up electing C or D when you could have had B by voting sincerely.
"“One person, one vote” mean that every enfranchised voter has an equal influence on government in elections because of our inherent equality as citizens and this is independent of any utilitarian notion of personal investment in the outcome.
If I enthusiastically prefer Candidate A and you prefer Candidate B only tepidly, your vote for Candidate B should count no less (nor more) than my vote for A."
I suppose that would be obvious to somebody who took the Condorcet criterion as axiomatic, but I don't, and the above restatement of it isn't obvious to me either. (I consider the Condorcet criterion a generally-desirable property of a voting system, not always outweighing other desirable properties.)
Among other things, the spectrum of strength of voter preferences affects voters' likelihood of voting at all. A clique of voters who all vote _does_ (and should!) have more say than a clique of "tepid" voters many of whom, although allowed and encouraged to vote, choose not to.
I don't think you can legitimately use the language of inequality and disenfranchisement in connection with things that are completely within the voter's power. If you don't bother voting, you have nobody to blame but yourself (in the absence of voter-suppression tactics). If you have the opportunity to rank five candidates on a ballot but choose to only rank two, you have nobody to blame but yourself for giving the system less signal than you could have given.
In any ranked-ballot system, the only way to express a "strong" or "weak" preference between two candidates is to rank more or fewer candidates between them. If a voter ranks C, D, and E between A and B, it _could_ mean the voter really doesn't care and has ranked several of them randomly, but it's much more likely to mean that the voter prefers A over B more strongly than A over the others, and/or the others over B. If (most) voters give us this added signal, why shouldn't we use it to give them what they say they want?
> In any ranked-ballot system, the only way to express a "strong" or "weak" preference between two candidates is to rank more or fewer candidates between them.
Some systems allow you to rank candidate equally, which is an expression of indifference, and some allow you to leave some candidates unranked, which is an expression of a strong preference against them.
>In any ranked-ballot system, the only way to express a "strong" or "weak" preference between two candidates is to rank more or fewer candidates between them.
Well, it's a preference differential between the two candidates. I'm just saying that we can all just *say* our preference is enthusiastic and our vote should be counted more. Just because I *say* my vote should be counted more than it would otherwise be counted, doesn't mean that my vote *should* be counted more than it would otherwise be counted.
Too many people have died for the principle of valuing our votes equally. Our votes should be equal and count equally because we are both human beings of inherently equal value. It shouldn't matter that my support for my candidate is more enthusiastic than your support for your candidate. Your vote and my vote should count the same. Otherwise, if we cannot have equally-valued votes, then I want my vote to count more than yours.
Sure, our votes *should* be equal and count equally, but they never will be in practice because some people will just not vote. Even if you made voting mandatory, some people would write in "Mickey Mouse" or vote randomly. You can't force people to express a preference they sincerely don't have.
"we can all just *say* our preference is enthusiastic"
Yes, that's exactly the point, we *can* all say that. *Everyone* has the right and the ability to say that. It's your choice -- not somebody else's -- how much say you have. *That's* what "too many people died for". The franchise is not the act of voting; it's the *right* to vote (in practice, without intimidation or suppression).
Let's make this concrete, using not ranked voting but score voting, where you can assign a number of points to each candidate independently. If you're allowed to give up to 10 points to each candidate and you give your top choice only 3 points, *nobody stopped you* from giving that choice 10 points; you simply chose to express less of a preference than you could have. (Likewise if you give *every* candidate 10 points, you've expressed no preference at all.) The only reason to do that is if your sincere preference really is weak, and if it were much weaker you wouldn't have voted at all. You've voluntarily given the system information about your sincere preference; why should the system ignore that information and treat you as having a stronger preference than you really do?
Now back to ranked voting. As mentioned above, the only way to express a weak preference between A and B is to rank few candidates between them; the only way to express *only* weak preferences is to rank few candidates at all. But still, if you have a strong preference, nobody is preventing you from expressing it; if you don't, nobody but yourself has taken away your voice.
A voting system is supposed to extract a group preference from a bunch of individual preferences, but it is at best only as good as the information it's given. Single-vote plurality gives the system very little information to work with; a ranked or value system allows voters to give much more information about their preferences. Of course, you could choose to ignore most of that information, count only top rankings, and do single-vote plurality anyway. You could ignore slightly less information and do Instant Runoff. You could ignore even less information and do Condorcet. Or you could ignore still less information and do Borda. Why should the system not use as much information as voters are willing to give it?
> If I enthusiastically prefer Candidate A and you prefer Candidate B only tepidly, your vote for Candidate B should count no less (nor more) than my vote for A.
Yes it absolutely should. Who are you declare that my mild preference for B > A should have the same weight as your strong preference for A > B? If I want to express a weak preference, I should be free to do so. My weak preference should not be arbitrarily forced to have the same weight as your strong preference; that is undemocratic.
>>> My weak preference should not be arbitrarily forced to have the same weight as your strong preference; that is undemocratic. <<<
What's democratic is that no enfranchised person is lifted above another in the same election. If our votes are not going to count the same, then I want my vote to count more than yours. If that is unacceptable to you, the *only* manner that neither of us can claim we are being undemocratically screwed is to count our votes equally. Strictly equally. Because of our equality as persons.
Neither of us are royalty. Or a privileged class of voters. In the civil rights struggle, too many people have died in the United States in the pursuit of the equality of their vote.
> If our votes are not going to count the same, then I want my vote to count more than yours.
Yes, and if I want my preference between two candidates to count less than yours, or to be recorded as indifference, then that is my right. You don't get to arbitrarily increase the strength of my vote so that it changes the outcome in a way I don't want.
> Also, I don’t take it as axiomatic that electing the Condorcet winner where one exists is always right
If you're using ranked ballots, then yes, it is always right. You need score ballots if you want information about how strongly one candidate is preferred over another.
> it doesn’t matter much how you pick the Condorcet winner; there’s no particular advantage to brackets over counting wins in a round-robin tournament.
Exactly. So ranked bracket voting is a better system because it's easier to count and easier for voters to understand, which is far more important than any theoretical difference between Condorcet methods.
“If you're using ranked ballots, then yes, it is always right. You need score ballots if you want information about how strongly one candidate is preferred over another.”
Sure, score ballots _could_ provide more information about the strengths of preferences, in exchange for some of the same problems as approval voting: candidates persuading their supporters to approve _only_ that candidate, and give everyone else a zero, reducing the system to single-vote plurality.
Ranked ballots do provide information about the strength of preferences: if I rank A>B>C>D, you can be reasonably confident that my preference for A over D is stronger than my preference for B over C, even if you can’t quantify how much stronger. Assuming that every step in a ranking represents an equal amount of preference is an oversimplification, but at least as justifiable as any other way to do it.
And if we have strength-of-preference information, even if a little fuzzy, I would argue that the Condorcet winner is not necessarily the “right” choice: a candidate who gets a lot of first-place votes but also a lot of last-place votes is probably more divisive and will have a harder time governing than a candidate whom fewer voters love but nobody hates.
It’s pretty rare for Borda to not choose a Condorcet winner when one exists. When it happens, it’s usually that scenario: a loved-and-hated candidate against one who’s both less loved and less hated.
“ranked bracket voting is a better system because it's easier to count and easier for voters to understand”
Neither of those is obvious to me. Voting systems have to be perceived as fair, or people won’t accept the results. The perception (even if it seldom matters in practice) that somebody could rig the outcome by manipulating the brackets makes this system problematic.
> candidates persuading their supporters to approve _only_ that candidate, and give everyone else a zero
1. Why would any candidate attempt that?
2. Why would any voter agree to it?
I don't see any incentive to do that.
> If I rank A>B>C>D, you can be reasonably confident that my preference for A over D is stronger than my preference for B over C
Yes, I agree. Letting voters express it directly is better, though.
> And if we have strength-of-preference information, even if a little fuzzy, I would argue that the Condorcet winner is not necessarily the “right” choice
Yes, I agree.
> Neither of those is obvious to me. Voting systems have to be perceived as fair, or people won’t accept the results.
Brackets are perceived as fair. They are ubiquitous in sports and other competitions.
> The perception (even if it seldom matters in practice) that somebody could rig the outcome by manipulating the brackets makes this system problematic.
That's why they are chosen randomly after ballots have been cast.
"> candidates persuading their supporters to approve _only_ that candidate, and give everyone else a zero
1. Why would any candidate attempt that?"
To maximize that candidate's chance of winning. Sure, most candidates also have a vested interest, in their capacity as citizens, in who wins if they don't, but they have a *much stronger* vested interest in winning themselves (it's their job and their career after all). This isn't hypothetical: in actual Approval Voting elections, actual candidates have put up billboards exhorting people to approve Joe Schmoe and nobody else.
"2. Why would any voter agree to it?"
Because the voter, for whatever reason, has become a "fan" or "follower" of that particular candidate, to the point of subordinating the voter's own interest to the candidate's. Because the voter is basically lazy and would be happier with single-vote plurality. Face it, we all know people like that.
"Brackets are perceived as fair. They are ubiquitous in sports and other competitions."
Yes, brackets are ubiquitous in sports and other competitions, where the consequences (for other than the players themselves) are merely bragging rights. That doesn't mean they're fair, and one can easily imagine a choice of brackets that "unfairly" advantages one team over another; see my initial comment at the top of this thread. And of course, most team sports can only use binary choices: there are only two teams in a football game, so the analogues of ranked and approval voting aren't even on the table.
"That's why they are chosen randomly after ballots have been cast."
In the aftermath of the 2020 election, the Trump campaign challenged a bunch of voting practices in court, sometimes suggesting that a whole district's Presidential votes were irremediably tainted and should be thrown out altogether. They did this only in districts Biden had won heavily, within states Biden had won narrowly -- in other words, after you've seen the votes as actually cast, you pick and choose which ones to throw out in order to maximize your chance of changing the winner. The same thing happened with the North Carolina Supreme Court race in 2024: after the ballots were counted, the loser (by hundreds of votes) argued that tens of thousands of ballots from specific categories of people should be invalidated, in order to "get a second swing at the ball". (Not to be partisan here: Democratic candidates have done the same thing, because the way the rules are written, it's the rational thing to do if you can.)
_Anything_ chosen after ballots have been cast is susceptible to rigging behind the scenes. Indeed, anything chosen after there are solid opinion-poll results is susceptible to rigging, e.g. gerrymandering, voter suppression by neighborhood and by race, etc. Even if you know and I know that the bracketing algorithm is truly random, how much faith does the average voter have in that? Better to not even have the appearance of a possibility of rigging.
Okay, Ned, thank you for writing this. Specifically:
"The ballot in an Instant Bracket Voting election could look the same as ballots in any Ranked-Choice Voting election. The voters would rank the candidates in order of preference, ..."
We must make it clear that, in this case, this *is* a form of Ranked-Choice Voting and not allow FairVote to appropriate the umbrella term to mean only Instant-Runoff Voting. Personally, I think that's the *only* way Instant Bracket Voting can be done. Expecting voters who never ever think about March Madness or athletic tournaments to fill out brackets on their ballot is not going to fly. Not in my opinion. It has to be a ranked-ballot, RCV. (But not IRV.)
But then the question I have is this: We know that this is Condorcet-consistent, so we know that no matter how it's seeded, if there is a Condorcet winner (which is 99% of the time) that Condorcet winner will be elected. But if there is *no* Condorcet winner, the outcome of the election will depend on how the first round is seeded. That's a problem. The method should be deterministic and not depend at all on a random manner of who gets matched up with whom.
That's why I think that Round Robin (or what I might call "straight-ahead Condorcet") is fairer and clearer than Instant Bracket Voting. And if there *is* a cycle, it's not exactly a tie unless the votes were perfectly symmetrical between the candidates involved in the cycle (the Smith set).
Consider a Round-Robin Tournament that ends up lacking a Condorcet winner. If it were hockey or basketball or wrestling, they could do as Nic Tideman suggests and favor the matches with scores having wider margins over the matches with smaller margins as a basis for identifying the champion. Or Minimax.
Two years ago, I was able to get a Vermont legislator and counsel to write a Condorcet RCV bill and we were considering Bottom Two Runoff IRV vs. a straight-ahead Condorcet (with Plurality for the contingency that there is no Condorcet winner). https://legislature.vermont.gov/Documents/2024/Docs/BILLS/H-0424/H-0424%20As%20Introduced.pdf
The BTR-IRV was attractive because it is the smallest modification to Hare IRV that makes IRV Condorcet-consistent and the modification is easily understood, It's also a Single-method Condorcet system. It just does what it does and someone is elected. If there is a Condorcet winner, that candidate will be elected. If there isn't, someone is still elected with this single method.
The reason we settled on a Two-method Condorcet system was because this legislator, the legislative counsel, and I all agreed that "The law should say what it means and mean what it says."
It seemed that straight-ahead Round Robin, with language to meaningfully resolve a cycle, would be easiest for everyone to understand and to buy into it. If there ever was a cycle, most people would accept the resolution of the cycle as fair. If I were to do it again (and we might do it again this session, I dunno), I think it would be Condorcet-TTR for top-two runoff instead of Condorcet-Plurality. That would make it elect the Hare IRV winner in the case of a cycle involving just the top three candidates.
But I'm a little nervous about this Instant Bracket Voting if there is a Condorcet cycle and the outcome depends on how the candidates are seeded. It shouldn't.
https://arxiv.org/abs/2101.03455
RSEB has some strategy-resistance properties, too (though I don't claim to understand them)
https://luckorcunning.blogspot.com/2025/02/would-less-polarized-electorate-be-more.html
Interesting idea. I’m concerned that bracket voting is heavily sensitive to how the brackets are constructed: at least in cases where there’s no clear Condorcet winner, different algorithms for constructing the brackets could produce different winners, so whoever controls those algorithms has an opportunity to control the election.
You compare instant bracket voting with instant runoff voting, of which I’m a lukewarm fan. How does instant bracket voting compare to Borda-count ranked voting (which is also relatively easy to explain)? IIRC, Borda almost always picks the Condorcet winner where there is one, but needs no tie-breaking mechanism; more importantly, there’s no separate “build the brackets” step providing opportunities for manipulation.
The rare cases where Borda disagrees with Condorcet are because Condorcet asks which of two candidates each voter prefers, but ignores the additional information of _how strongly_ they prefer one over another; it treats the head-to-head comparison of a 4th-ranked and a 5th-ranked candidate the same as the comparison of a 1st-ranked and a 10th-ranked candidate. Suppose 49% of voters rank Bob in last place (in a field of three or more) and Chris first, while 51% rank Bob first and Chris second. Bob is the Condorcet winner, but Borda, using more information, picks Chris.
Brackets are more familiar and easier to understand, and Condorcet cycles are rare, so I think familiarity trumps any such concerns.
The sports analogy is exactly why I think people might distrust this system. I suspect that Condorcet cycles are more common in sports than in politics: I can easily see Team A having strengths that enable it to beat Team B, which has strengths that enable it to beat Team C, which has strengths that enable it to beat Team A. And I can easily see fans of team A feeling cheated that team C was matched first against A rather than B.
Also, I don’t take it as axiomatic that electing the Condorcet winner where one exists is always right; see the last paragraph of my previous comment.
But if you do accept the Condorcet criterion, then precisely because Condorcet cycles are rare, it doesn’t matter much how you pick the Condorcet winner; there’s no particular advantage to brackets over counting wins in a round-robin tournament.
> "But if you do accept the Condorcet criterion, then precisely because Condorcet cycles are rare, it doesn’t matter much how you pick the Condorcet winner; there’s no particular advantage to brackets over counting wins in a round-robin tournament."
I'm in general agreement, being a Condorcet advocate.
Cycles are rare. Appear to be less than 1% (2 RCV elections in the US so far have been a Rock-Paper-Scissors cycle. 2 other RCV elections had a Condorcet winner but IRV failed to elect the CW.)
It's most important to *get* RCV reformed to be Condorcet-consistent than worrying about which Condorcet method. Hard core geeks seem to like Schulze the best. I like Ranked-Pairs. But I was able to get my legislator to introduce a Condorcet RCV bill and then it appeared that, given the initial suspicion of RCV and a "new RCV", that then it was important for the law to simply say what it means and mean what it says. That meant a two-method system where the simple round-robin pairwise contest intended to identify the one candidate who never loses to anyone. And in the case that no such Condorcet winner exists, then a simple, straight rule perceived to be fair (like Plurality or Top-Two Runoff) is used. Then the intent of the law is most apparent from the legislated language.
Okay, Stephen,
> "The rare cases where Borda disagrees with Condorcet are because Condorcet asks which of two candidates each voter prefers, but ignores the additional information of _how strongly_ they prefer one over another; ..."
Condorcet pointed out that voters will strategically exaggerate the relative strength in preference to increase the odds for their candidate. Borda is inherently vulnerable to strategic Burying, as is Score Voting or any cardinal system (even Approval Voting).
Borda's defense was "My system is only intended for honest men." That is weak. We need the system to be invulnerable (as much as possible) to nefarious or strategic actions of dishonest persons. We don't want the system to be gamed.
> "... it treats the head-to-head comparison of a 4th-ranked and a 5th-ranked candidate the same as the comparison of a 1st-ranked and a 10th-ranked candidate. "
As it should. “One person, one vote” mean that every enfranchised voter has an equal influence on government in elections because of our inherent equality as citizens and this is independent of any utilitarian notion of personal investment in the outcome.
If I enthusiastically prefer Candidate A and you prefer Candidate B only tepidly, your vote for Candidate B should count no less (nor more) than my vote for A. The effectiveness of one’s vote – how much their vote counts – is not proportional to their degree of preference but is determined only by their franchise. A citizen with franchise has a vote that counts equally as much as any other citizen with franchise.
For any ranked ballot, this means that if Candidate A is ranked higher than Candidate B then that is a vote for A, if only candidates A and B are contending (such as in the RCV final round). It doesn’t matter how many levels A is ranked higher than B, it counts as exactly one vote for A.
"Condorcet pointed out that voters will strategically exaggerate the relative strength in preference to increase the odds for their candidate. Borda is inherently vulnerable to strategic Burying, as is Score Voting or any cardinal system (even Approval Voting)."
Yes, there are scenarios in which Borda rewards insincere voting, and you're quite right that appealing to "honest men" is a feeble argument. But those scenarios are rare, and they depend on knowing with some precision how everybody else is going to vote. If you don't know how everybody else is going to vote (especially difficult if they might vote insincerely too!), Borda tends to punish insincere voting in the most appropriate way: by giving you what you said you wanted. If you sincerely feel A > B > C > D but vote A > C > D > B to boost A's chances, and A turns out to have less support than you estimated, you may end up electing C or D when you could have had B by voting sincerely.
"“One person, one vote” mean that every enfranchised voter has an equal influence on government in elections because of our inherent equality as citizens and this is independent of any utilitarian notion of personal investment in the outcome.
If I enthusiastically prefer Candidate A and you prefer Candidate B only tepidly, your vote for Candidate B should count no less (nor more) than my vote for A."
I suppose that would be obvious to somebody who took the Condorcet criterion as axiomatic, but I don't, and the above restatement of it isn't obvious to me either. (I consider the Condorcet criterion a generally-desirable property of a voting system, not always outweighing other desirable properties.)
Among other things, the spectrum of strength of voter preferences affects voters' likelihood of voting at all. A clique of voters who all vote _does_ (and should!) have more say than a clique of "tepid" voters many of whom, although allowed and encouraged to vote, choose not to.
I don't think you can legitimately use the language of inequality and disenfranchisement in connection with things that are completely within the voter's power. If you don't bother voting, you have nobody to blame but yourself (in the absence of voter-suppression tactics). If you have the opportunity to rank five candidates on a ballot but choose to only rank two, you have nobody to blame but yourself for giving the system less signal than you could have given.
In any ranked-ballot system, the only way to express a "strong" or "weak" preference between two candidates is to rank more or fewer candidates between them. If a voter ranks C, D, and E between A and B, it _could_ mean the voter really doesn't care and has ranked several of them randomly, but it's much more likely to mean that the voter prefers A over B more strongly than A over the others, and/or the others over B. If (most) voters give us this added signal, why shouldn't we use it to give them what they say they want?
> In any ranked-ballot system, the only way to express a "strong" or "weak" preference between two candidates is to rank more or fewer candidates between them.
Some systems allow you to rank candidate equally, which is an expression of indifference, and some allow you to leave some candidates unranked, which is an expression of a strong preference against them.
Hay, I'm sorry for missing this.
>In any ranked-ballot system, the only way to express a "strong" or "weak" preference between two candidates is to rank more or fewer candidates between them.
Well, it's a preference differential between the two candidates. I'm just saying that we can all just *say* our preference is enthusiastic and our vote should be counted more. Just because I *say* my vote should be counted more than it would otherwise be counted, doesn't mean that my vote *should* be counted more than it would otherwise be counted.
Too many people have died for the principle of valuing our votes equally. Our votes should be equal and count equally because we are both human beings of inherently equal value. It shouldn't matter that my support for my candidate is more enthusiastic than your support for your candidate. Your vote and my vote should count the same. Otherwise, if we cannot have equally-valued votes, then I want my vote to count more than yours.
Sure, our votes *should* be equal and count equally, but they never will be in practice because some people will just not vote. Even if you made voting mandatory, some people would write in "Mickey Mouse" or vote randomly. You can't force people to express a preference they sincerely don't have.
"we can all just *say* our preference is enthusiastic"
Yes, that's exactly the point, we *can* all say that. *Everyone* has the right and the ability to say that. It's your choice -- not somebody else's -- how much say you have. *That's* what "too many people died for". The franchise is not the act of voting; it's the *right* to vote (in practice, without intimidation or suppression).
Let's make this concrete, using not ranked voting but score voting, where you can assign a number of points to each candidate independently. If you're allowed to give up to 10 points to each candidate and you give your top choice only 3 points, *nobody stopped you* from giving that choice 10 points; you simply chose to express less of a preference than you could have. (Likewise if you give *every* candidate 10 points, you've expressed no preference at all.) The only reason to do that is if your sincere preference really is weak, and if it were much weaker you wouldn't have voted at all. You've voluntarily given the system information about your sincere preference; why should the system ignore that information and treat you as having a stronger preference than you really do?
Now back to ranked voting. As mentioned above, the only way to express a weak preference between A and B is to rank few candidates between them; the only way to express *only* weak preferences is to rank few candidates at all. But still, if you have a strong preference, nobody is preventing you from expressing it; if you don't, nobody but yourself has taken away your voice.
A voting system is supposed to extract a group preference from a bunch of individual preferences, but it is at best only as good as the information it's given. Single-vote plurality gives the system very little information to work with; a ranked or value system allows voters to give much more information about their preferences. Of course, you could choose to ignore most of that information, count only top rankings, and do single-vote plurality anyway. You could ignore slightly less information and do Instant Runoff. You could ignore even less information and do Condorcet. Or you could ignore still less information and do Borda. Why should the system not use as much information as voters are willing to give it?
> If I enthusiastically prefer Candidate A and you prefer Candidate B only tepidly, your vote for Candidate B should count no less (nor more) than my vote for A.
Yes it absolutely should. Who are you declare that my mild preference for B > A should have the same weight as your strong preference for A > B? If I want to express a weak preference, I should be free to do so. My weak preference should not be arbitrarily forced to have the same weight as your strong preference; that is undemocratic.
>>> My weak preference should not be arbitrarily forced to have the same weight as your strong preference; that is undemocratic. <<<
What's democratic is that no enfranchised person is lifted above another in the same election. If our votes are not going to count the same, then I want my vote to count more than yours. If that is unacceptable to you, the *only* manner that neither of us can claim we are being undemocratically screwed is to count our votes equally. Strictly equally. Because of our equality as persons.
Neither of us are royalty. Or a privileged class of voters. In the civil rights struggle, too many people have died in the United States in the pursuit of the equality of their vote.
> If our votes are not going to count the same, then I want my vote to count more than yours.
Yes, and if I want my preference between two candidates to count less than yours, or to be recorded as indifference, then that is my right. You don't get to arbitrarily increase the strength of my vote so that it changes the outcome in a way I don't want.
> Also, I don’t take it as axiomatic that electing the Condorcet winner where one exists is always right
If you're using ranked ballots, then yes, it is always right. You need score ballots if you want information about how strongly one candidate is preferred over another.
> it doesn’t matter much how you pick the Condorcet winner; there’s no particular advantage to brackets over counting wins in a round-robin tournament.
Exactly. So ranked bracket voting is a better system because it's easier to count and easier for voters to understand, which is far more important than any theoretical difference between Condorcet methods.
“If you're using ranked ballots, then yes, it is always right. You need score ballots if you want information about how strongly one candidate is preferred over another.”
Sure, score ballots _could_ provide more information about the strengths of preferences, in exchange for some of the same problems as approval voting: candidates persuading their supporters to approve _only_ that candidate, and give everyone else a zero, reducing the system to single-vote plurality.
Ranked ballots do provide information about the strength of preferences: if I rank A>B>C>D, you can be reasonably confident that my preference for A over D is stronger than my preference for B over C, even if you can’t quantify how much stronger. Assuming that every step in a ranking represents an equal amount of preference is an oversimplification, but at least as justifiable as any other way to do it.
And if we have strength-of-preference information, even if a little fuzzy, I would argue that the Condorcet winner is not necessarily the “right” choice: a candidate who gets a lot of first-place votes but also a lot of last-place votes is probably more divisive and will have a harder time governing than a candidate whom fewer voters love but nobody hates.
It’s pretty rare for Borda to not choose a Condorcet winner when one exists. When it happens, it’s usually that scenario: a loved-and-hated candidate against one who’s both less loved and less hated.
“ranked bracket voting is a better system because it's easier to count and easier for voters to understand”
Neither of those is obvious to me. Voting systems have to be perceived as fair, or people won’t accept the results. The perception (even if it seldom matters in practice) that somebody could rig the outcome by manipulating the brackets makes this system problematic.
> candidates persuading their supporters to approve _only_ that candidate, and give everyone else a zero
1. Why would any candidate attempt that?
2. Why would any voter agree to it?
I don't see any incentive to do that.
> If I rank A>B>C>D, you can be reasonably confident that my preference for A over D is stronger than my preference for B over C
Yes, I agree. Letting voters express it directly is better, though.
> And if we have strength-of-preference information, even if a little fuzzy, I would argue that the Condorcet winner is not necessarily the “right” choice
Yes, I agree.
> Neither of those is obvious to me. Voting systems have to be perceived as fair, or people won’t accept the results.
Brackets are perceived as fair. They are ubiquitous in sports and other competitions.
> The perception (even if it seldom matters in practice) that somebody could rig the outcome by manipulating the brackets makes this system problematic.
That's why they are chosen randomly after ballots have been cast.
"> candidates persuading their supporters to approve _only_ that candidate, and give everyone else a zero
1. Why would any candidate attempt that?"
To maximize that candidate's chance of winning. Sure, most candidates also have a vested interest, in their capacity as citizens, in who wins if they don't, but they have a *much stronger* vested interest in winning themselves (it's their job and their career after all). This isn't hypothetical: in actual Approval Voting elections, actual candidates have put up billboards exhorting people to approve Joe Schmoe and nobody else.
"2. Why would any voter agree to it?"
Because the voter, for whatever reason, has become a "fan" or "follower" of that particular candidate, to the point of subordinating the voter's own interest to the candidate's. Because the voter is basically lazy and would be happier with single-vote plurality. Face it, we all know people like that.
"Brackets are perceived as fair. They are ubiquitous in sports and other competitions."
Yes, brackets are ubiquitous in sports and other competitions, where the consequences (for other than the players themselves) are merely bragging rights. That doesn't mean they're fair, and one can easily imagine a choice of brackets that "unfairly" advantages one team over another; see my initial comment at the top of this thread. And of course, most team sports can only use binary choices: there are only two teams in a football game, so the analogues of ranked and approval voting aren't even on the table.
"That's why they are chosen randomly after ballots have been cast."
In the aftermath of the 2020 election, the Trump campaign challenged a bunch of voting practices in court, sometimes suggesting that a whole district's Presidential votes were irremediably tainted and should be thrown out altogether. They did this only in districts Biden had won heavily, within states Biden had won narrowly -- in other words, after you've seen the votes as actually cast, you pick and choose which ones to throw out in order to maximize your chance of changing the winner. The same thing happened with the North Carolina Supreme Court race in 2024: after the ballots were counted, the loser (by hundreds of votes) argued that tens of thousands of ballots from specific categories of people should be invalidated, in order to "get a second swing at the ball". (Not to be partisan here: Democratic candidates have done the same thing, because the way the rules are written, it's the rational thing to do if you can.)
_Anything_ chosen after ballots have been cast is susceptible to rigging behind the scenes. Indeed, anything chosen after there are solid opinion-poll results is susceptible to rigging, e.g. gerrymandering, voter suppression by neighborhood and by race, etc. Even if you know and I know that the bracketing algorithm is truly random, how much faith does the average voter have in that? Better to not even have the appearance of a possibility of rigging.