[EM] Letter to an author of a voting system article

[MIKE OSSIPOFF]

I sent this comments letter to the author of an article on voting systems:

I agree that the best voting systems use rank-ballotiong. Regrettably, 
Instant Runoff (IRV) is not one of those best voting systems.

Though the best methods use rank balloting, the merit of a rank-balloting 
voting system depend entirely on how the rankings are counted.

It turns out that only a very few of the very best rank-methods are as good 
as the simple & modest Approval method:

Approval:

Voters may mark as many names on the the ballot as they want to. The 
candidate receiving the most marks wins.

[end of Approval definition]

A more familiar method that is strategically equivalent to Approval is 
"Cardinal Ratings" (CR). CR is the familiar points system, sometimes called 
"Range Voting":

Voters may give to any candidate(s) any number of points, within some 
pre-specified range. The candidate receiving the most points wins.

For instance, voters could be allowed to give to any candidate anywhere from 
0 to 10 points, or from 0 to 100 points, or anywhere from -10 to 10 points, 
or anywhere from -100 to 100 points.

Approval itself is a version of CR. Approval is the simplest CR version, the 
0,1 CR version in which a voter may give to any candidate either 0 or 1 
point.

Being more familiar than Approval, the CR versions such as 0 to 10 or 0 to 
100, or -10 to 10, or -100 to 100 would probably be the best public proposal 
for voting system reform.

As I said, only a very few of the very best rank-methods are as good as 
Approval and CR.

You can read about those at:

http://www.barnsdle.demon.co.uk/vote/sing.html

IRV has a number of problems that its advocates don't tell you about.

They boast that IRV gets rid of the lesser-of-2-evils problem, and that you 
can safely vote your favorite in 1st place. No, that's only true if your 
favorite is a sure loser, sure to be the first candidate eliminated. 
Otherwise your favorite could eliminate your needed compromise, and then 
lose to your last choice.

IRV fails the following criterion:

Participation:

Adding to the count one or more ballots that vote X over Y should never 
change the winner from X to Y.

[end of Participation definition]

Approval and CR pass Participation. Instant Runoff (IRV) fails 
Participation.

The rank methods that are better than Approval and CR are certain versions 
of Condorcet's method.

In particular, the "winning-votes" versions of Condorcet's method.

Condorcet was the 18th century French founder of voting theory. Here's the 
general definition of winning-votes Condorcet's method:

1. Voters may rank any number of candidates in order of preference. They may 
rank more than one candidate at the same rank position if they want to.

2. X "beats" Y if more voters rank X over Y than rank Y over X.

3. Any candidate who is unbeaten wins, and if there's any such candidate, 
the count ends.

4. Otherswise, one of several "circular tie solutions" is used.

5. For the purpose of those methods, a "defeat" is an instance of one 
candidate beating another.

6. For the purpose of those circular tie solutions, if X beats Y, the 
"strength" of that defeat is defined as the number of people who ranked X 
over Y.
[end of general definition of winning-votes Condorcet's method]

Here are two circular tie solutions:

Plain Condorcet (PC) is the literal interpretation of the circular tie 
solution described by Condorcet himself:

Plain Condorcet (PC):

Drop the weakest defeat. Repeat till a candidate isn't beaten. S/he wins.

[end of PC definition]

Sequential Dropping (SD):

Drop the weakest defeat that's in a cycle. Repeat till a candidate is 
unbeaten. S/he wins.

[end of SD definition]

These Condorcet methods meet criteria not met by other proposed methods, 
including Instant Runoff.

Here are some such criteria:

Weak Defensive Strategy Criterion (WDSC):

If a majority prefer X to Y, then they should have a way of voting that 
ensures that Y won't win, without any member of that majority voting a 
less-liked candidate over a more-liked one.

[end of WDSC definition]

All the Condorcet versions that I propose meet WDSC. Instant Runoff fails 
WDSC, and so does Plurality, the method currently in use.

Strategy-Free Criterion (SFC):

First a preliminary definition:

The Condorcet winner (CW) is a candidate who, when compared separately to 
each one of the others, is preferred to him/her by more voters than 
vice-versa.

[end of CW definition]

SFC:

If no one falsifies a preference, and if a majority prefer the CW to 
candidate Y, and vote sincerely, then Y shouldn't win.

[end of SFC definition]

What SFC means is that, when a method is used that complies with SFC, a 
majority, under the plausible premise conditions of SFC, has no need to do 
other than rank the candidates sincerely. They need no strategy under those 
conditions.

It's desirable for a group of voters to be completely free of need to do 
other than rank sincerely. SFC describes the conditions under which it's 
possible to make that guarantee, for methods that comply with SFC.

SFC's definition refers to voting sincerely, and so a definition of that is 
needed too:

A voter votes sincerely if s/he doeesn't falsify a preference, or fail to 
vote a preference that the balloting system in use would have allowed 
him/her to vote in addition to the preferences that s/he actually did vote.

[end of sincere voting definition]

A voter votes X over Y if s/he votes in such a way that if we count only 
his/her ballot, with all the candidates by X & Y deleted from it, X wins and 
Y doesn't win.

[end of definition of voting one candidate over another]

A voter falsifies a preference if s/he votes X over Y and prefers Y to X.

A voter votes a preference for X over Y if s/he prefers X to Y and votes X 
over Y.

[end of supporting definitions]

Favorite Betrayal Criterion (FBC):

In a given election, for any particular voter who has a unique favorite, and 
with a particular set of candidates, there should be no possible 
configuration of other people's votes such that that voter can get his/her 
best outcome only by voting someone over his/her favorite.

[end of FBC definition]

In other words, no one should ever need to vote someone over his favorite.


Approval & CR meet FBC, Participation, and WDSC.

PC and SD meets SFC and WDSC.


More methods and criteria can be read about at:

http://www.barnsdle.demon.co.uk/vote/sing.html

Let me know if there are any questions, comments, objections, or 
disagreements.

Mike Ossipoff

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