<div dir="auto">The median rating step satisfies independence of clones, like Majority Judgment. It just uses a different tiebreaker.<div dir="auto"><br></div><div dir="auto"><a href="https://electowiki.org/wiki/Majority_Judgment">https://electowiki.org/wiki/Majority_Judgment</a><br></div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Fri, Jan 5, 2024, 00:27 Hahn, Paul <<a href="mailto:manynote@wustl.edu">manynote@wustl.edu</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
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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.<br>
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<div dir="ltr">--pH</div>
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<blockquote type="cite">On Jan 4, 2024, at 10:47 PM, Ted Stern <<a href="mailto:dodecatheon@gmail.com" target="_blank" rel="noreferrer">dodecatheon@gmail.com</a>> wrote:<br>
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<div dir="auto">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. </div>
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<div dir="ltr" class="gmail_attr">On Thu, Jan 4, 2024, 16:42 Joshua Boehme <<a href="mailto:joshua.p.boehme@gmail.com" target="_blank" rel="noreferrer">joshua.p.boehme@gmail.com</a>> wrote:<br>
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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.<br>
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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<br>
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Step 4 in particular might be where this matters (which could affect subsequent steps)<br>
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On 1/2/24 18:12, Ted Stern wrote:<br>
> Continuing my search for a summable voting method that discourages burial<br>
> and defection, I've come across this hybrid of Condorcet and median ratings<br>
> that acts like Smith/Approval with an automatic approval cutoff. I'm<br>
> calling it Pairwise Median Rating (PMR), but it could also be described as<br>
> Smith//MR//Pairwise//MRScore:<br>
> <br>
> 1. Equal Ranking and ranking gap allowed (essentially a ratings method<br>
> with rank inferred). For purposes of this discussion, assume 6 slots (5<br>
> ranks above rejection).<br>
> 2. In rank notation for this method, '>>' refers to a gap. So 'A >> B'<br>
> means A gets top rank while B gets 3rd place. Similarly '>>>' means a gap<br>
> of two slots: 'A>>>B' means A is top ranked while B is in 4th place.<br>
> 3. [Smith]<br>
> 1. Compute the pairwise preference array<br>
> 2. The winner is the candidate who defeats each other candidate<br>
> pairwise.<br>
> 3. Otherwise, drop ballots that don't contain ranks above last for<br>
> any member of the Smith Set.<br>
> 4. [Median Rating]<br>
> 1. Set the MR threshold to top rank.<br>
> 2. While no Smith candidate has a majority of undropped ballots at or<br>
> above the threshold, set the threshold to the next lower rank,<br>
> until there<br>
> is no lower rank.<br>
> 3. The winner is the single candidate that has a majority of<br>
> undropped ballots at or above the threshold.<br>
> 5. [Pairwise]<br>
> 1. Otherwise, if more than one candidate passes the threshold, look for<br>
> a pairwise beats-all candidate among candidates meeting the MR threshold.<br>
> (i.e. Condorcet on just the MR threshold set).<br>
> 2. If there is one, you have a winner.<br>
> 6. [MR Score]<br>
> 1. Otherwise, the winner is the Smith set candidate with the largest<br>
> number of ballots at or above the Median Rating threshold (their MRscore).<br>
> <br>
<br>
...<br>
<br>
> PMR passes Condorcet Winner, Condorcet Loser, IIB, and is cloneproof.<br>
> I believe it passes LNHelp. It probably fails Participation and IIA.<br>
> There are probably weird examples where changing one vote changes the<br>
> MR threshold. But overall, I think it has a good balance of incentive<br>
> to deter burial and deliberate cycles.<br>
<br>
> <br>
> <br>
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