[EM] No evidence that IRV doesn't fail. Reasons why it must.

Dgamble997 at aol.com Dgamble997 at aol.com
Thu Jan 22 16:44:02 PST 2004


In response to my post you gave the following example of an IRV failure:

100: CDBEA

This type of example is not unfamiliar to me ( it or something very like it ) 
turned up several times in a series of posts called " The Turkey Problem " 
and "Is Condorcet The Turkey?" that ran (in circles) for months during your 
period of retirement.

This first example is countered with a second example which is usually 
something like:

47 A>B>C
4  B>A>C
2  B>C>A
47 C>B>A

in which B is the Condorcet winner with a very low percentage of the first 
preference vote.

In the first example IRV will probably elect the wrong candidate.

In the second example Condorcet will probably elect the wrong candidate.

So why do I think the Condorcet winner is correct in the first example and 
the IRV winner in the second?

It is a question of the utility of the candidates. Ranked ballots show that 
candidate A is preferred to B but not how much candidate A is preferred to 
candidate B. A could have a utility of 1.0 and B a utility of 0.9 or A could have 
a utility of 1.0 and B a utility of 0.4. A low first preference vote Condorcet 
winner could well be a low utility, non-entity candidate whose only virtue is 
that he/she offends nobody. Why not use Cardinal Ratings instead? Because 
Cardinal Rating is very subject to manipulation and there is a strong incentive 
to rank candidates only at the top and bottom of the scale. Why not use 
Approval instead then? This solves the strategy problems but makes the method 
insensitive by only giving the voters only two levels of utility.

Basically every single winner method you can think of has both problems of 
strategy and problems of legitimacy of winner. Some have arguably more problems 
than others (Borda) and Plurality most of all, but all have problems. Which 
problems you subjectively consider important decides both which criteria you 
consider important and which methods you think are good.

You wrote:

>Let's simplify this by only showing the preferences that IRV actually looks 
>at and counts:

>50: AB
>51: B
>100: C
>53: D
>49: ED

>It looks rather sparse, doesn't it, when we leave out people's voted 
>preferences that IRV doesn't count.

Yes IRV does ignore information. But there is also a problem with Condorcet 
in this respect too. Take for example the ballot paper A>B>C>D>E. In the 
pairwise comparisons the fourth choice D counts 1 against E in the pairwise 
comparison, A the first choice also counts 1 in any pairwise comparison. Candidates A 
and D are not of equal utility to the voter that is why A is 1st and D 4th yet 
their votes both count at a value of 1 in the pairwise comparisons. Condorcet 
uses all the information but treats it as equal in the pairwise comparisons 
when it clearly is not.

You also wrote:

>You make it sound as if IRV's inadequacy were somehow unavoidabale. But it's 

>merely the avoidable result of the fact that the busiest promoters won't 
>take the trouble to educate themselves.

Whatever single winner system you choose some sort of inadequacy is 
unavoidable whether it's the loss of an election under Condorcet WV due to offensive 
order reversal or a Condorcet winner being eliminated in a 3 candidate IRV count 
as a result of having just less than 1/3 of the vote. With single method 
methods the elimination of one problem more often than not leads to the creation 
of another.

You also said:

>Anyone claiming that those plausible & ordinary situations won't happen 
>often should explain why they believe that.

>Though there aren't recorded and publislhed data that would show how often 
>these failures are happening in existing IRV elections, it's a sure thing 
>that they'll happen regularly

You are correct these situations will indeed happen under IRV as surely as 
low utility winner situations will occur under Condorcet. The kind of situation 
you had been referring to in your previous posts was that of Favourite 
Betrayal. Looking at Australian elections I have found little if any evidence of 
this. In South Australia in 1997 in a number of seats both National/Liberal or 
Labor could have defeated the other's candidate by voting Australian Democrat ( 
examination of the transfer patterns in seats where the AD's came second showed 
that over 80% of Liberal/National voters preferenced the AD's over Labor and 
vice-versa). This didn't happen. You yourself are not going to betray Nader in 
order to help a mainstream Democrat beat Bush.

David Gamble

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