[EM] Pairwise Median Rating

[Ted Stern]

The median rating step satisfies independence of clones, like Majority
Judgment. It just uses a different tiebreaker.

https://electowiki.org/wiki/Majority_Judgment

On Fri, Jan 5, 2024, 00:27 Hahn, Paul <manynote at wustl.edu> wrote:

> I would think to be considered resistant to cloning strategy the opposite
> would need to be true as well; that is, cloning a winning candidate
> shouldn’t make them lose, either.
>
> --pH
>
> On Jan 4, 2024, at 10:47 PM, Ted Stern <dodecatheon at gmail.com> wrote:
>
> 
> 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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