[EM] Rethinking Burial Detection Runoff

[Forest Simmons]

Chris,

I like your new Condorcet method, and consider it to be a much more
practical suggestion than any of my sincere CW finder ideas currently in
progress.

The ballot profile you provided to illustrate your LV Sorted Margins burial
resistant method, ended up electing A, which we considered to be better
than electing B, because we thought that with some positive probability the
ballot profile might be a result of the B faction's insincere order
reversal .... changing sincere 44 B>A to 44 B>C, i.e. the B faction burying
A under C ... so that electing B, like just about every other method under
the sun, would encourage bad behavior.

Is it insulting to voters to build in safe guards that make insincere
truncations or burials less likely to pay?

Is it insulting to lock your front door when leaving town for a few dsys?

Borda famously said, "My method is intended for honest voters." [He was
aware of the burial incentive, but like Saari, Maskin, and many others,
apparently unconcerned about the Clone Dependence problem.]

You and I prefer methods that encourage honest voters to stay honest... and
a bicycle lock makes stealing your bike less attractive, but cannot
guarantee protection against the determined thief.

What your example profile shows is that no Universal Domain method can
determine whether or not a ballot set of complete rankings is the result of
burial of a sincere CW.

In fact, to convert B to ballot CW only takes five "unburials" : 5 C>A -->
5 C>B.  while to change C to the ballot CW takes 46 unburials: 46 A>B -->
A>C, and it takes 44 unburials to convert A into the ballot CW: 44 B>C -->
44 B>A.

It looks like B is at least as likely as A to be the sincere CW, if there
is one.  But it is impossible to know for sure without some information
outside of the Universal Domain. ... perhaps some kind of sincere runoff,
or asking Alexa, for example.

Going outside the strict Universal Domain by allowing truncations, equal
rankings, approval cutoffs, or other levers, offer additional
expressiveness that can reduce incentives for burial, compromise, etc.

I've been experimenting with how far we can get with two sets of ballots
... one possibly strategic set, for the purpose of determing the finalists
and runoff order ... and the other set dedicated solely to the kind of
runoff that elects the sincere CW whenever there is one.

And geometric considerations show that when the ballot Smith set has fewer
than four candidates, the existence of a sincere CW is much more likely
than not.

That's why my currently focus is on a three candidate (i.e. worst case
public Smith set) runoff method for which the sincere CW (when there is
one) is the game theoretic winner (assuming perfect information and
rational voting).

Next time, a method that will seem more familiar!

fws





On Wed, Jun 14, 2023, 5:19 PM C.Benham <cbenham at adam.com.au> wrote:

> 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
> >
> >
> >
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20230614/5873f88f/attachment.htm>