Douglas Greene douggreene at earthlink.net
Fri Aug 17 09:55:04 PDT 2001

------Warren D. Smith 2001--------

Some nasty examples of the Hare-STV (Single Transferable Vote;
also called IRV=Instant Runoff Voting; in United Kingdom has also
been called "alternative vote") system in action.

No-show paradox: 
If X's supporters do not show up to vote for X,
that may cause X to win - while if they do vote, that can cause X to lose!

Here is an example of 2 nasty things in an IRV election
[SJ Brams: Voting procedures, ch. 30 pp.1050-1090 in
vol 2 Handbook of Game theory, ed. R.Aumann and S.Hart,
Elsevier Science, NY 1992] Let the votes be
 A>B>C>D  7 votes
 B>A>C>D  6
 C>B>A>D  5
 D>C>B>A  3
In the Hare-STV=IRV voting system: A wins.
1. This is despite fact B is Condorcet winner, i.e. would win direct
pairwise elections versus every opponent!
2. If the 3 voters in the last row instead had
ranked D first - but refused to say more, i.e. refused to provide 
their 2nd 3rd 4th choices -
then B would have won (which those voters prefer over A).
This illustrates the fact that in IRV, voters can be motivated to
refuse to rank-order some of the candidates, thus defeating IRV's purpose
of garnering ordering information from the voters.
And: if these 3 voters instead had dishonestly voted
A>D>C>B  then B would have won (which they'd prefer to A)
despite fact they just RAISED their opinion of A to
first place and nothing else changed! That is
an example of "non-monotonicity".
This same reference, in its section 5, also gives some other 
nasty examples illustrating no-show, etc.  

Comparison with range voting:
Range voting (and every additive system) is always monotonic
so that there is never a dis-incentive to show up to vote.

Multiple-districts paradox:
also in the literature called the "consistency" problem:
if 2 subsets of the voters agree on a winner, to be consistent, the
combined election should produce that same winner - but
with the IRV, that is not necessarily so.
OK, I just cooked up an example by fiddling with the
example above...

District I:
A wins:
 A>B>C>D  70 votes
 B>A>C>D  60
 C>B>A>D  53
 D>C>B>A  9

District II:
A wins:
 A>D>C>B  8
 D>B>A>C  5

The combination of both districts is won by B in IRV voting.

Comparison with range voting:
Meanwhile range voting (and every additive system) is always 
self-consistent in this sense. (It is harder to manipulate election 
results by artificial district-drawing, in consistent voting systems.)

Dishonest voting is the best strategy in 3-candidate IRV election:
Suppose the votes among the 348 other voters for
the 3 candidates A,B,C are
 C>A>B: 150;
 B>C>A: 50;
 A>B>C: 99;
 B>A>C: 49.
In this case a voter's 1 additional  A>B>C
honest vote would cause  B  to be eliminated in STV round 1,
at which point  C  would beat  A  in the next and final round by
200 to 149. However, if our voter had
dishonestly voted  B>C>A,  then
A  would have been eliminated in round 1, at which point
B  would win the final round versus  C,  199 to 150.
In this case, our voter's honest C-last vote
actually caused C to win!
[Example is from paper "range voting" by Warren D. Smith.]
In this example, the alternative dishonest vote
B>A>C  also works; thus here again, artificially and dishonestly
ranking the most-disliked (C) of the two frontrunners (B,C)
artificially "last" is a best strategy for this voter.

Comparison with range voting:
In a 3-candidate Range-voting (or approval voting) election, 
the best voter strategy is always to vote with an ordering
not inconsistent with your honest ordering.

Effect of strategic voters who try not to "waste their vote"

A final and very important remark on strategic voting is this.
A very common voter strategy, adopted by voters who do not want
to "waste their vote", is to artificially rank the most-liked and 
most-hated among the two perceived frontrunners "first" and "last",
even if the voter does not really think those two candidates are
the best and worst. It is precisely this voter strategy which causes 
3rd party candidates to have no chance in the "plurality voting"
system currently in use throughout in the US.

Now, the final THEOREM in my paper [Warren D. Smith: "Range Voting"]
(which I first noticed empirically in my computer simulations), is
that this strategy, if it is adopted by almost all voters,
causes the same election winner as would happen in plurality voting,
ALSO always to be the winner in STV voting, Condorcet-LR voting,
and various other systems (but not range and not approval).

In other words, in this very important sense, STV is NOT an 
improvement over plurality voting at all, and in fact it is equivalent!
So the "Green Party", if it is trying to create a voting system capable
of electing 3rd party candidates in the presence of lots of this kind of
strategic voters, is therefore making the wrong move by pushing for
STV voting in Oregon! They should be pushing range voting.

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