[EM] Nightmare On IRV Street ?

Adam Tarr atarr at purdue.edu
Thu Jul 3 22:54:10 PDT 2003

David Gamble wrote:

>All single seat methods are capable of producing bad results.

Of course, they are only bad from some point of view.  But yes, I'd agree 
with that in principle.  That said, some will produce bad results much more 
reliably than others.

>This is why I believe that single member methods should only be used for 
>single offices ( mayor, governor, president, etc) and that multi-member 
>bodies should be elected by proportional representation. There is nothing 
>and can be nothing that is proportional about the allocation of a single seat.

That's a laudable goal.

>  My preferred single member method is IRV.

That's a pretty big non sequitur there.  Why IRV?  Simply because that's 
what the largest US electoral reform group supports?

Can you really put the Condorcet "nighmare" scenario I wrote in the same 
ballpark as the IRV nightmare scenario?  My Condorcet scenario ends with 
the compromise candidate winning, and nobody regretting their vote.  In the 
IRV scenario I showed, the clearly, indisputably preeminent candidate 
loses, and a third of the electorate is kicking themselves on election night.

>My preferred multi-member method is the single transferable vote. It is 
>considered an important principle in STV that lower preferences should 
>neither help nor harm higher preferences. The reason for this is that if 
>by casting a lower preference you can defeat a higher preference you are 
>given a powerful incentive not  to cast lower preferences.

This is also true of winning votes Condorcet the vast, vast majority of the 
time.  The scenario you mention below is no exception.

>For example:
>44 A>B>C
>7 B>A>C
>7 B>C>A
>42 C>B>A
>The election was to close to call, before the votes were counted it was 
>uncertain whether A or C would obtain the most first preferences ( and 
>also irrelevant considering A and C supporters second preferences).
>Under Condorcet by casting a second preference for compromise candidate B 
>both A and C voters have effectively defeated their first choice and elected B.

This is totally untrue.  As Kevin pointed out, they have only beaten the 
OTHER candidate, their least favorite, by casting second place 
votes.  Nobody in this election was hurt by their second place votes.  Not 
in the slightest.

>Yes, I am aware that B is the most generally preferred candidate and that 
>by voting for B C supporters have also defeated A.

That is, in fact, the only thing they have done.

>If a A and C voters had not expressed a 2nd preference and voted
>44 A
>7 B>A>C
>7 B>C>A
>42 C
>A would have won, or if two votes had been cast differently C would have won.

Sure, and in either scenario the losing faction says to themselves, "why 
didn't I vote for B?"  It can only help them, and can never hurt 
them.  Here, I'll show the decision matrix.  The top row is the vote of the 
A supporters, and the left column is the votes of the C supporters.  The 
corresponding matrix entry is who wins the election.  (This may look lousy, 
but if you cut and paste into something that has monotype spacing it will 
look fine):

----| A   | A>B |
C   | A   | A   |
C>B | B   | B   |

Now, if C happens to have more first place support than A, the matrix in 
stead looks like this:

----| A   | A>B |
C   | C   | B   |
C>B | C   | B   |

Now, lets combine the two matrices and show what the possibilities for each 
faction are.   The result for each faction if A has more votes are before 
the slash, and after the slash is if C has more votes.

----| A   | A>B |
C   | A/C | A/B |
C>B | B/C | B/B |

So, for the A faction, voting their full preferences changes the result 
from C winning to B winning, or keeps the result the same.  Similarly, for 
the C faction, voting their full preferences changes the result from A 
winning to B winning, or keeps the result the same.  Voting a second 
preference will NEVER cause an adverse result for a faction in this election.

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