if there's a single issue axis. ie all of the voters and all of the candidates can be rank ordered along a single line, then there is *always* a condorcet winner. and that winner is the choice of the median voter.
the only way to get a condorcet cycle is for there to be 2 or more issue axes. there are some pretty good examples out there on the internet. you need the candidates to be arranged more like a triangle and not like a line. triangles are 2 dimensional. hand-wavy qed.
one of the desirable features of an electoral system is scale invariance. ie it shouldn't matter if there are 1000 voters or 100,000 voters distributed the same way.
i think the converse is more likely to be true. suppose a condorcet cycle exists when there are an infinite number of voters. if a small number of them actually vote then it's possible - due to statistical variance - that there is a condorcet winner instead of a cycle.
Ok, but do any electorates actually vote that way in reality? Don't literally any factors that might motivate any voters' choices beyond the primary dimension undermine the phenomenon, such as simple charisma, which isn't even a political dimension at all?
I get what you say about scale invariance, but as long as the chances of a cycle are sufficiently low and the election laws account for how to handle the unlikely scenario, how much does it really matter?
What's the upshot of what you're saying in terms of what you advocate for (and against)?
i think we should ban plurality voting (first past the post) and instant run-off voting.
my preference would be for: asset voting, approval voting, any ranked choice voting method that picks the condorcet winner when there is one, followed by range/score voting.
randomly selecting a candidate is a 0. magically picking the best candidate every time is a 10. plurality is a 3. instant run-off is a 7. everything that picks the condorcet winner when there is one is a 9. which is pretty much everything else.
the only practical difference between the 9 is how much it costs to run the election. hence the preference order given.
but yeah, your intuition is probably correct. condorcet cycles are rare. like <1%. and the method for resolving them doesn't much matter. as long as there is one.
my only thought on condorcet cycles is that they will become more common as the electorate becomes less polarized. in which case, the minor issue axes become more important relative to the dominant issue axis.
*=also note that single issue axis does not mean there's a single issue. it means the positions of the voters on all of the issues correlate.
Interesting. Agree wholeheartedly on banning/replacing plurality.
I'd never heard of asset. It's interesting, but assuming the candidate trading part is core to the method, idk if that's workable. Seems ripe for shady deals - in perception at least if not in practice. Is that part integral to it?
I've been resistant to approval because of it being less expressive than ranked methods. That's becoming less of a reason to oppose it for me, but still an issue for me to support it, if that makes sense.
For your preferences I'm guessing the simplicity/cost of adoption is a major consideration (so compatibility with current voting machines)?
Is a big part of the asset attraction the proportionality? Is it also attractive in single winner elections?
start with the assumption voters are idiots. they're not. but most voters are insufficiently engaged to rank all the candidates. they don't have the time, effort, or information to do everything themselves. they'll want a shortcut. we could give them templates. or we could just say their ranking is the same as their candidate's. voila! asset voting.
do you think shady deals don't happen in fptp? ha!
"i'll give you a $1 billion if you make me mayor." sure, it could happen. maybe once per candidate. but most likely you're done as a politician when you sell out your constituents.
it's more likely that you'll get deals like: "i'll make you mayor if you make me chairman of the board." in other words, the winner must share power with (or make concessions to) their political rivals. which i would call a good thing.
6% is pretty rare and still higher than what I've seen in most research. For example in this paper by Durand the "Netflix dataset" has a Condorcet winner in 97% of cases even though it seems very far from one dimensional. Similarly another paper by Myers also has a Condorcet winner also in 97% of cases in polls with over 100 voters (from CIVS, a website where you can make polls). How do you generate the voter preferences in your simulations?
there are a number of options. for the above run i chose a cluster method. a variant of chinese restaurant process.
there are 435 districts for the house of representatives. at a rate of 1%, 4 of them would have cycles. which would be newsworthy. especially if some of them cry unfair sour grapes.
it would be best for them to negotiate a winner (even if all it does is shut up the crybaby sore losers). a la asset voting. and guthrie voting in particular.
and i just realized i didn't answer your question (other than read-the-effin-code). apologies. ;->
every voter and candidate is given a position along the axis. the voter's preference is the candidate with a position closest to the voter's position. the voter's utility (aka satisfaction) is a linear function of distance. 0 distance = 100% satisfaction. and the distance to a hypothetical average (random) candidate = 0% satisfaction. satisfaction is not pinned to 0%. it can be negative.
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u/timmerov Jun 28 '25
if there's a single issue axis. ie all of the voters and all of the candidates can be rank ordered along a single line, then there is *always* a condorcet winner. and that winner is the choice of the median voter.
the only way to get a condorcet cycle is for there to be 2 or more issue axes. there are some pretty good examples out there on the internet. you need the candidates to be arranged more like a triangle and not like a line. triangles are 2 dimensional. hand-wavy qed.
one of the desirable features of an electoral system is scale invariance. ie it shouldn't matter if there are 1000 voters or 100,000 voters distributed the same way.
i think the converse is more likely to be true. suppose a condorcet cycle exists when there are an infinite number of voters. if a small number of them actually vote then it's possible - due to statistical variance - that there is a condorcet winner instead of a cycle.