<div dir="auto">Monotone Banks methods are not easy to come by ... but here is the simplest UD Monotone Banks method that I know of:<div dir="auto"><br></div><div dir="auto">MaxPS Sorted Pairwise</div><div dir="auto"><br></div><div dir="auto">Initialize a list variable L as the list of candidates in order of their MaxPairwiseSupport.</div><div dir="auto"><br></div><div dir="auto">[Break ties by considering in turn 2nd, 3rd, ... levels of support.]</div><div dir="auto"><br></div><div dir="auto">While no member of L is pairwise undefeated, update L by removing its bottom member X as well as every candidate defeated by X.</div><div dir="auto"><br></div><div dir="auto">Elect the remaining undefeated candidate highest on the list L.</div><div dir="auto"><br></div><div dir="auto">It seems to me that this procedure yields a very clean, monotone, clone-free, one pass, precinct summable, Banks efficient, UD, burial resistant method.</div><div dir="auto"><br></div><div dir="auto">Are we over-looking anything?</div><div dir="auto"><br></div><div dir="auto"><br></div><div dir="auto">fws</div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Sun, Jul 30, 2023, 6:21 AM Kristofer Munsterhjelm <<a href="mailto:km_elmet@t-online.de">km_elmet@t-online.de</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">Since it's pretty quiet at the moment, here's another observation. I've <br>
been testing some methods that pass DMT or DMTC, and I've found out two <br>
things:<br>
<br>
- The "monotonized" contingent vote, where if A is the Plurality winner <br>
and can give some of his first preferences to some other B to displace <br>
the other finalist C and get B into the top two instead, A's score <br>
becomes A>B instead of A>C, is not that much more strategy susceptible <br>
than the ordinary contingent vote (0.91 vs 0.87 for 97 candidates, 10k <br>
elections, 32k tries per election).<br>
<br>
- But it's much harder to get the true strategy resistance of <br>
nonmonotone methods, because coalitional strategy is much harder to find <br>
than two-sided "rank who you're compromising for top, the current winner <br>
bottom" strategy.<br>
<br>
So even if say, a method X and its monotone variant both have strategy <br>
resistance 0.8, it's often harder to execute strategy against the <br>
nonmonotone one in practice because you can overshoot.<br>
<br>
In a monotone method, if your honest vote is A>B>C>D>E, and the current <br>
winner is D, and you're compromising for C, then if A>C>B>D>E works, <br>
then C>A>B>D>E will also work and most likely C>A>B>E>D will also work. <br>
So you can slam your compromise to the top and your burial target (the <br>
current winner) to the bottom, and that's a pretty simple strategy.<br>
<br>
But in a nonmonotone method, it's possible that A>C>B>D>E will work but <br>
C>A>B>D>E won't. So even though the honest election is vulnerable to <br>
strategy with both methods, it's harder to find the correct strategy.<br>
<br>
Thus if you absolutely need all the strategy resistance you can get, <br>
nonmonotone is probably where it's at. I'll still try to find a good <br>
monotone burial-resistant method, though!<br>
<br>
Some stats to show this effect: impartial culture, 97 voters, 5 <br>
candidates, 50k elections, 32k coalitional tries per election:<br>
<br>
Smith,Contingent vote:<br>
Ties: 0.00612<br>
<br>
Burial without compromise: 0.11049<br>
Compromise without burial: 0.24123<br>
Burial and compromise: 0.00278<br>
Two-sided: 0.00254<br>
Other: 0.51588<br>
<br>
Total susceptibility: 0.87292<br>
<br>
Smith,Contingent vote with donation:<br>
Ties: 0.00904<br>
<br>
Burial without compromise: 0.13044<br>
Compromise without burial: 0.23402<br>
Burial and compromise: 0.01158<br>
Two-sided: 0.54180<br>
Other: 4e-05<br>
<br>
Total susceptibility: 0.91788<br>
<br>
The "Other" category (which contains pushover and pushover-like <br>
strategy) has been almost entirely emptied, and that strategy has become <br>
two-sided instead.<br>
<br>
(Two-sided is the fraction of elections where neither burial nor <br>
compromising works, but doing both at the same time works.)<br>
<br>
-km<br>
----<br>
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</blockquote></div>