[EM] Remembering the plain English

John B. Hodges jbhodges at usit.net
Tue Jul 8 08:03:07 PDT 2003

Greetings- It occurred to me this morning that a lot of Saari's 
mathematical critique of Approval voting may be beside the point. 
What is AV INTENDED to do? It (attempts to) pick the candidate that 
the greatest number of people regard as not unacceptable.

Contrast this with Plurality, which (attempts to) pick the candidate 
that the greatest number of people regard as the "best" candidate. Or 
Borda Count, which (attempts to) pick the candidate who beats the 
greatest number of other candidates in voters' individual rankings. 
(Borda count assigns a number to each candidate equal to the number 
of other candidates THAT candidate beats in THAT voter's ranking. 
These numbers are then summed for each candidate across all voters.) 
Or Condorcet-variation-x, which (attempts to) pick the candidate, if 
there is one, that would beat each of the others in a two-person 

Saari is making the point that a profile of voter's preferences, 
described in terms of ordinal rankings of the candidates, will 
usually not determine a unique winner under AV. Indeed in a wide 
variety of such profiles, AV could generate ANY POSSIBLE result, 
within the rules of AV, because AV gives the voters discretion to 
mark their ballots in several equally-legitimate ways. This may be 
true and may give you valuable insights into other properties of AV, 
but the profiles of voter's preferences, expressed as ordinal 
rankings, are strictly-speaking irrelevant to AV. To judge AV, you 
need voter's sets of "acceptable" and "unacceptable" candidates. This 
is not the same as their ordinal rankings, and cannot be derived from 

There are several relevant questions in judging these assorted voting 
methods. (1) What are they TRYING to accomplish, and IS that what YOU 
want to accomplish in the first place? (2) Do they succeed in what 
they are trying to accomplish? (3) What other effects and 
characteristics do they have, that might be relevant to your decision 
of which method to use?

A voting method may fail in its purpose because of "insincere" 
voting, by people trying to "game the system". It may fail due to 
voter confusion, or by just plain bad design. But, answering question 
2 should come after answering question 1. Is this method trying to do 
something that you want to do?

So, for example, The Approval-voting "nightmare" I quoted from Saari 
yesterday: 9,999 voters rank the candidates ABC, 1 ranks them CBA, 
all vote for their top two. B wins with 10,000 votes to A's 9,999. AV 
is here doing exactly what it set out to do; this is not a 
malfunction. I doubt any other voting method would do the same, but 
that is not surprising, because they are trying to do other things.
John B. Hodges, jbhodges@   @usit.net
The two-party system is obsolete and dysfunctional.
Better forms of democracy: www.fairvote.org

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