# [EM] Ordering defeats in Minimax

robert bristow-johnson rbj at audioimagination.com
Thu Apr 27 22:53:50 PDT 2017

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Subject: Re: [EM] Ordering defeats in Minimax

From: "Juho Laatu" <juho.laatu at gmail.com>

Date: Thu, April 27, 2017 6:15 pm

To: "Election Methods" <election-methods at lists.electorama.com>

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> I agree that it is important to understand how strong different pairwise preference results should be considered. In the generic preference function that I gave I to some extent tried to answer your question "How many voters were there?", and find a parameter (k) that could be
adjusted to set the balance right (between high number and low number of voters that indicated their preference). In the function ( (x-y)*(x+y)^k ) the "x-y" part sets the margins approach as a starting point. The "(x+y)^k" part can be seen as an adjustment factor that takes into
account the number of votes that had an opinion "x+y". Constant k tells us how much we should weaken (k>0) or strengthen (k<0) the pairwise comparison result in the case that not all voters gave their preference.
>
okay, i wanna restate this with the Wn and Ln symbols.

(W1, L1) > (W2, L2)   means

(W1-L1)*(W1+L1)^k   >   (W2-L2)*(W2+L2)^k

now, if k=0, this is the same as what i am coining as
"Arithmetic Margins" (for lack of a better term).  if k = -1, then it's the same as the percentage margin, where a larger race has no more weight than a smaller race if the percent margins are the same.  this is, i believe, going to have equivalent outcome as Markus's margins of
logarithms (what i coined "Geometric Margins").
If someone has better terminology for naming these different forms of margins, please correct my neologism before it takes root.

--
r b-j                  rbj at audioimagination.com
"Imagination is more important than knowledge."
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