[EM] Venzke system for applying criteria, "FARCS"

[Chris Benham]

This current discussion was sparked by my remark (March 17, 2007):

>I share the Venke (similar to Woodall's) approach that the criteria
>should assume that the voters intend to submit a ranked ballot (maybe 
>truncated, maybe with some equal-ranking) and that voters fill out 
>their actual (maybe restricted) ballots in a way that is consistent 
>with their intended ballots, and when ballot restrictions prevent
>voters from fully voting their intended ranked ballots the criteria are 
>based on the intended ballots.
>

Mike Ossipoff responded (March 20, 2007):

> What an elaborate counterfactual story. It’s amazing what lengths to 
> which some people will go, to make Plurality fail Condorcet’s 
> Criterion without mentioning preference.
>
> I've already answered about that. It's based on a privileged balloting 
> system. My criteria make no mention of any balloting system.
>
> Though you go to great lengths to avoid mentioning preferences, you 
> don't mind saying that the voter intends to vote a ranking, when s/he 
> votes in Plurality. I've talked to voters, and many of them are 
> adamantly opposed to any voting system other than Plurality. They 
> don't intend to vote a ranking when they vote Plurality. And that's 
> only part of the counterfactual nature of your fictitious-rankings 
> system of criteria.


Mike, notice that I specified that the voters' intended ranking is 
"maybe truncated". It doesn't matter if the voters subjectively
don't have "rank" in their vocabulary: those that plan to cast a valid 
Plurality vote intend to rank a single candidate above all others.

Whatever balloting system is used all votes (that make any distinction 
among the candidates) contain some (logically implicit)
ranking data and there is no other type of data that they all contain, 
so I can't see that your reference to a "privileged balloting
system" is a meaningful criticism.

Mike apparently didn't think that I or Kevin had properly defined 
Kevin's way of applying criteria, so he came up with
a definition of what he called "Fictitiously Assumed Rankings Criteria 
System (FARCS)".

Here is my attempt at a definition of the Venzke approach to applying 
criteria with Mike-satisfying precision:

> Venzke rules for demonstrating a voting method's failure of criterion X:
>
> Criteria are written in the form of "if A, then B" where A refers to 
> some stipulation about the votes and B refers to
> something about the election result that must happen.
>
> It is assumed that the voters have an 'intended ranking' of the 
> candidates that may be truncated and/or include some
> above-bottom equal ranking. By definition, if the balloting rules 
> allow the voters to fully express this ranking then
> that is what the voters will do.
>
> The "A" part of a criterion refers to this intended ranking.
>
> If the balloting rules don't allow the voters to fully express their 
> intended ranking, then we assume that the voters
> vote to express as much of it as the balloting rules allow, giving 
> priority to expressing as many of their intended
> strict pairwise preferences as possible followed by expressing as many 
> of their intended pairwise equal-preferenes
> (indifferences) as possible.
>
> If the voters can only express some or all of their intended ranking 
> by giving preference data that isn't on their
> intended ranking, then we assume that they do so in a way that 
> contradicts their intended ranking as little as
> possible.
>
> If in testing for a method's compliance with criterion X, we can 
> follow the above rules/assumptions and show
> an example of "A and not B", then we have proved that the method fails 
> criterion X.


Chris Benham