[EM] DH3 and honest Condorcet winners

robert bristow-johnson rbj at audioimagination.com
Sat Jul 17 21:03:34 PDT 2021

> On 07/17/2021 1:31 PM Kristofer Munsterhjelm <km_elmet at t-online.de> wrote:
> In the classical DH3 scenario, the dark horse is universally loathed by
> the voters. This suggests a smart-aleck way of making almost every
> method DH3-proof: just eliminate every candidate that don't have at
> least one first preference.

which, if you have 10,000 voters will never happen.  try flipping a coin and get heads 50 times in a row.  that's more likely to happen.

> Now suppose that we have an election after every faction has gone on its
> burial spree,

so voters are upping the Dark Horse that they loathe in an attempt to gain advantage over the other candidates they fear will beat their favorite?

> and there were initially some voters who ranked the dark
> horse first. It would look something like this:
> 34: A>X>B>C
> 33: B>X>C>A
> 32: C>X>A>B
>  5: X
> But this is just a three candidate version of the Left, Center, Right
> scenario. If X is a genuine consensus candidate, then X should be
> elected

and i cannot see how you can differentiate this scenario from the ostensible Dark Horse insincerely bumped up.

> and a failure to do so is an instance of center squeeze. But if
> this is the aftermath of a DH3 scenario, then X must absolutely not be
> elected.

listen, if we cannot differentiate a sincere mark on a ballot from an insincere mark, we should not try to.  but we *should* have systems and rules that do not predictable incentivize insincere marking.

Arrow or Gibbard or Satterthwaite aside, we should examine what are common or likely scenarios that would incentivize strategic voting and not use contrived and highly unlikely specific scenarios in policy making to evaluate voting systems.

it's the most threatening hazards that we should try to avoid.

outside of a cycle, and valuing equal voter influence in elections, what is a *realistic* hazard that would challenge the main election ethic of elections, that is to determine the majority will of the electorate and elect a candidate so that the minority voters' votes do not count more than the majority voters' votes?

I think, to be honest, we should accept the marked ballots as sincere and count X as the genuine consensus candidate and the only Consistent Majority Candidate (which is what the CW is) there is.

If more voters mark their ballots preferring Candidate A over Candidate B than the number of voters marking their ballots to the contrary, then there is no consistently good reason why Candidate B should be elected (again, assuming we're nowhere near a cycle).

I cannot think of a good reason ever to not elect the Condorcet Winner when the ballot data clearly indicates that some candidate is the CW.  When a cycle happens, then perhaps there is some subtlety in electing a candidate without rewarding bad strategic voting behavior.  But I really think that a cycle will never happen in a governmental election and, while we should have law that will elect someone even without a CW in the outcome.  It's just that I would weight that problem scenario with a very small probability of occurrence.


r b-j . _ . _ . _ . _ rbj at audioimagination.com

"Imagination is more important than knowledge."


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