aaronI'll share a troubling fact with you if you share one with me
The McKelvey–Schofield chaos theorem proves that, if an electorate is presented with a series of proposed policy changes and everyone votes according to their honest preference, the proposals can be fashioned and ordered in such a way that any policy can be made to win—even one that no voter prefers to the starting point.
AatubeCould you source the "even one that no voter prefers to the starting point" part?
en.wikipedia.org/…/McKelvey–Schofield_chaos_theor…
There will in most cases be no Condorcet winner and any policy can be enacted through a sequence of votes, regardless of the original policy. This means that adding more policies and changing the order of votes (“agenda manipulation”) can be used to arbitrarily pick the winner.
The article doesn’t explicitly say that this includes policies not preferred by any single voter, but it’s implied by “any” and “arbitrary” (and can be verified by the original theorems).
I'm not too familiar in the field, but doesn't a policy have to appeal more to a specific base than its appeal to another base to cause a Cordocet tie?
Yeah, the Condorcet criterion is a lot more restrictive in the space of policies (where you can make incremental changes in any direction) than in elections for a discrete set of candidates. (Which is why they say that in most cases there won’t be one.)
Yeah, so in my understanding of that, doesn’t that mean the winning policy has to appeal more to a voter base than one that appeals to another voter base?
That’s true for any pairwise vote, but not for the entire sequence.
As in the Condorcet paradox, voter preferences are intransitive: voters preferring A to B and B to C doesn’t imply that voters will prefer A to C. But where the Condorcet paradox shows how this can lead to a cyclical subset of candidates where no candidate can beat all other members of the subset, the chaos theorem shows how this can lead to a series of votes that ends absolutely anywhere.
But if it is a paradox, then every proposal that still stands has to have beaten another proposal at least once. Thus I don't see how it could be one nobody has preferred at the start.
It’s not like Condorcet’s scenario where every candidate has a pairwise election against every other candidate—it assumes a subversive agenda-setter who presents each new proposal as a yes-or-no alternative to the existing status quo (the previously-accepted proposal). Once a policy is rejected, it isn’t re-introduced.