[EM] Election methods scholarship

[Joseph Malkevitch]

Dear Robert,

Thanks for your comments on the slides that I prepared for a 50 minute verbal presentation for an audience that had no background regarding mathematical insights into voting and election situations. To avoid lots of "detail" I said verbally that I would typically restrict my attention to voting situations where the voters ranked all the alternatives without indifference. In that setting if there are 3 alternatives there are 6 ballot types. The way I count there are 13 types of ballots with three choices, no truncation and indifference allowed.

In "informal" discussions often words will be interpreted by different people differently. Even in more scholarly environments sometimes there is "sloppy" terminology. A good example is the use of the term Borda or Borda Count. This account:

https://en.wikipedia.org/wiki/Borda_count

May not be the same as what one might see elsewhere using the terms Borda or Borda Count. Mathematics tries to be "precise" but you can find mathematics books where the word trapezoid defiines different collections of quadrilaterals.

Regards,

Joe

________________________________
From: robert bristow-johnson <rbj at audioimagination.com>
Sent: Thursday, March 26, 2026 5:53 PM
To: Joseph Malkevitch <jmalkevitch at york.cuny.edu>; Joseph Malkevitch via Election-Methods <election-methods at lists.electorama.com>; Election Methods Mailing List <election-methods at electorama.com>
Subject: Re: [EM] Election methods scholarship

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Hay Joseph,

Some corrections to https://web.york.cuny.edu/~malk/ranked-voting-math-club-2022.pdf  :

On p 28, you said: "ii. preference, ordinal, or ranked ballot List choices in preference order without ties. Sometimes one is limited as to the total number of candidates one can rank (five for NYC voting)"

In fact, whether ties are allowed or not do not depend solely on whether is "preference" or "ordinal" or a ranked ballot.  It depends on the method.  Most Condorcet methods do not disallow equal rankings.  IRV, Borda, or Condorcet methods that are modifications of IRV may disallow equal ranking.  But straight-ahead Condorcet (with some appropriate completion method) or Ranked Pairs or Schulze or Minimax do not have a problem with equal rankings.

On p 39, the methods you shown are *not* "cardinal ballots".  They are ordinal ballots.  Only Score (incl. STAR) and Approval are cardinal ballots.

On p 41, there are *9* possible ways to mark your ballot with 3 candidates (or 10, if we count a blank ballots or "undervotes").  Not 6.

Since you were asking for feedback...

bestest,

--

r b-j . _ . _ . _ . _ rbj at audioimagination.com

"Imagination is more important than knowledge."

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