<div dir="auto">Thanks for opening up new vistas!<div dir="auto"><br></div><div dir="auto">How about restricting method X to Smith?</div><div dir="auto"><br></div><div dir="auto">Or using some other method to pare down the field to manageable size?</div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Tue, Aug 1, 2023, 4:21 PM 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">This is method X, the monotone burial-resistant method from the previous <br>
post: (It doesn't really have a name yet.)<br>
<br>
- Each candidate A obtains his score by eliminating candidates in <br>
rounds, one candidate per round, until one other candidate (B) remains <br>
or A himself is forced to be eliminated. In the former case, A's score <br>
is A>B. In the latter case, A's score is zero.<br>
<br>
- When figuring out A's score, the method chooses the sequence of <br>
candidates to eliminate so as to maximize that score.<br>
<br>
- In a round, the method can never eliminate a candidate who has more <br>
than 1/n of the total number of (non-exhausted) first preferences, where <br>
n is the number of remaining candidates in the round in question.<br>
<br>
- Unlike IFPP, it never eliminates more than one candidate per round.<br>
<br>
- Highest score wins.<br>
<br>
That's it!<br>
<br>
Now for the bad news:<br>
- it's not summable (a summary takes O(n2^n) space),<br>
- it's not polytime (ditto),<br>
- its use of quotas means it would probably fail IIB,<br>
- and I have no idea why it works.<br>
<br>
I can't say I wasn't tempted to name it after myself since it's kind of <br>
a big deal (if I can verify its monotonicity), but given its drawbacks, <br>
maybe it's not a good idea? It's like the Kemeny of monotone <br>
burial-resistant methods: slow and impractical, but it shows what's <br>
*possible*.<br>
<br>
I would very much like some independent verification or replication, though.<br>
<br>
-km<br>
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</blockquote></div>