[EM] Pairwise Median Rating

[Joshua Boehme]

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.

> 
> 
> ----
> Election-Methods mailing list - see https://electorama.com/em for list info