[EM] Pairwise Median Rating

[Ted Stern]

By cloneproof, I mean that turning a single candidate into either perfect
or effective clone groups will ever enable a candidate in that group to win
when they would lose as a single candidate. That is, resistant to cloning
strategy.

On Thu, Jan 4, 2024, 16:42 Joshua Boehme <joshua.p.boehme at gmail.com> wrote:

> Cloneproof in what sense? Perfect clones (voters rank them as tied)? Or
> effective clones (voters never rank another candidate between them)? For a
> system like this, those might not be equivalent.
>
> Suppose two factions of the Purple Party each field a candidate -- one for
> New Purple, and one for traditional Purple. Voters might draw meaningful
> distinctions between them even if they never rank a non-Purple candidate
> between them
>
> Step 4 in particular might be where this matters (which could affect
> subsequent steps)
>
>
>
> On 1/2/24 18:12, Ted Stern wrote:
> > Continuing my search for a summable voting method that discourages burial
> > and defection, I've come across this hybrid of Condorcet and median
> ratings
> > that acts like Smith/Approval with an automatic approval cutoff. I'm
> > calling it Pairwise Median Rating (PMR), but it could also be described
> as
> > Smith//MR//Pairwise//MRScore:
> >
> >     1. Equal Ranking and ranking gap allowed (essentially a ratings
> method
> >     with rank inferred). For purposes of this discussion, assume 6 slots
> (5
> >     ranks above rejection).
> >     2. In rank notation for this method, '>>' refers to a gap. So 'A >>
> B'
> >     means A gets top rank while B gets 3rd place. Similarly '>>>' means
> a gap
> >     of two slots: 'A>>>B' means A is top ranked while B is in 4th place.
> >     3. [Smith]
> >        1. Compute the pairwise preference array
> >        2. The winner is the candidate who defeats each other candidate
> >        pairwise.
> >        3. Otherwise, drop ballots that don't contain ranks above last for
> >        any member of the Smith Set.
> >     4. [Median Rating]
> >        1. Set the MR threshold to top rank.
> >        2. While no Smith candidate has a majority of undropped ballots
> at or
> >        above the threshold, set the threshold to the next lower rank,
> > until there
> >        is no lower rank.
> >        3. The winner is the single candidate that has a majority of
> >        undropped ballots at or above the threshold.
> >     5. [Pairwise]
> >     1. Otherwise, if more than one candidate passes the threshold, look
> for
> >        a pairwise beats-all candidate among candidates meeting the MR
> threshold.
> >        (i.e. Condorcet on just the MR threshold set).
> >        2.  If there is one, you have a winner.
> >     6. [MR Score]
> >     1. Otherwise, the winner is the Smith set candidate with the largest
> >        number of ballots at or above the Median Rating threshold (their
> MRscore).
> >
>
> ...
>
> > PMR passes Condorcet Winner, Condorcet Loser, IIB, and is cloneproof.
> > I believe it passes LNHelp. It probably fails Participation and IIA.
> > There are probably weird examples where changing one vote changes the
> > MR threshold. But overall, I think it has a good balance of incentive
> > to deter burial and deliberate cycles.
>
> >
> >
> > ----
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> info
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