[EM] Rethinking Burial Detection Runoff

[C.Benham]

Forest,

I am not enthusiastic about this idea.

> 46 A>B
> 44 B>C
> 5 C>A
> 5 C>B

In this example all the voters gave their full strict rankings. It isn't 
like a cycle was caused by a lot of truncation (or equal-ranking
possible Compromising) and we can say "Some of you may not have felt 
sufficiently informed about all the candidates or you forgot
this isn't FPP, so we are gong to have a runoff."

Instead we are saying "We think it highly likely that some of you are 
lying so we are going to make you vote again."

Too cynical and insulting.

One of the relatively simple methods I like has been named after me.  It 
says  "This is confusing. Can the the favourite of the fewest
please go away."

To get on the ballot at all in public political elections candidates 
normally have to show that they have some minimum exclusive
first preference support, but the Condorcet criterion is happy to elect 
a candidate with none.

Here is my new suggested Condorcet method:

*Voters rank from the top however may candidates they wish, equal 
ranking and truncation allowed. Also they may indicate an
approval cutoff, so they can rank among unapproved candidates. Default 
is approving all candidates ranked above at least one candidate.

If there is no CW, ignore rankings among unapproved candidates. If there 
is still no CW, then (based on the full rankings) elect the 
Smith//Approval winner.*

Chris Benham


On 14/06/2023 11:59 am, Forest Simmons wrote:
> Critiques by Kevin Venzke and Chris Benham have caused me to rethink 
> my approach to detection of a buried CW.
>
> To see the extent of the difficulty, let's reconsider one of Benham's 
> example profiles:
>
> 46 A>B
> 44 B>C
> 5 C>A
> 5 C>B
>
> There are three possible unilateral burial explanations for the ABCA 
> cycle:
>
> 1. Sincere 46 A>C --> 46 A>B
> 2. Sincere 44 B>A --> 44 B>C
> 3. Sincere 5 C>A --> 5 C>B
>
> If we are to depend on a final sincere binary runoff to determine the 
> sincere CW, which two candidates should be the finalists?
>
> Instead, I suggest a different kind of ballot that will detect a 
> sincere CW under the assumption of rational voters in possession of 
> perfect information about each other's sincere preferences.
>
> For Chris's example profile the new tangled ballot might look like ...
>
> B?(C?A)
>
> There are only four valid ballot submission possibilities:
>
> B>(C>A)
> B>(C<A)
> B<(C>A)
> B<(C<A)
>
> The instructions are (for each question mark), to answer the indicated 
> question by replacing the question mark with an inequality mark.
>
> It can be shown that if B is the sincere CW, a majority of the 
> rational voters will replace the first question mark with ">".
>
> Otherwise, the final runoff choice, answering the question C?A, will 
> determine the winner.
>
> For rational voters the other ballot possibilities, including; A?(B?C) 
> aas well as C?(A?B), would (theoretically) work just as well to elect 
> the sincere CW.
>
> What in general is the best psychological policy for setting up the 
> decision tree?
>
> Is it to set apart the RP winning votes alternative?
>
> Or perhaps the implicit approval chain climbing winner ... or perhaps 
> the Sequential Pairwise Elimination winner ... with or without "takedown."
>
> fws
>
>
>