Example with contrary half preference votes

Hugh R. Tobin htobin at ccom.net
Wed Jul 10 21:50:58 PDT 1996

Mike Ossipoff wrote:
> Say we were using Condorcet's method, with the added provision,
> recently proposed, that if a ballot ranks X & Y equally, below
> everything else in the Smith set, then that ballot is counted
> as casting half a vote for X over Y, & half a vote for Y over
> X.
> Sincere rankings:
> 46%: Dole, Clinton, Nader
> 20%: Clinton
> 34%: Nader, Clinton, Dole
> Dole voters truncate:
> 46%: Dole
> 20%: Clinton
> 34%: Nader, Clinton
> With the compulsory contrary half preferences provision,
> Dole wins. Without it, Clinton wins. Clinton is the Condorcet
> winner, & Dole is the only candidate over whom a majority
> has ranked someone else. GMC, Trunation-Resistance, &
> LO2E-1 are violated if the contrary half preferences provision
> is applied.
> But, if the contrary preference votes are _optional_, and
> if those criteria are re-stated, replacing "order-reversal"
> with "voting of a false preference", and if using the
> contrary half prefernces option is regarded as voting a
> false preference, then those re-defined criteris would then
> be met. TRC, for instance, would be met because it would
> no longer be just truncation that's giving the election to
> Dole; it would be truncation & false preference voting.
> GMC would be met if we regard the person using that option
> as ranking Nader over Dole--as he is in fact doing with
> half of a preference vote. So Condorcet with that contrary
> unvoted half preference votes provision could meet reasonably
> re-written versions of those criteria. But the contrary half
> preference votes should be optional.

> --[snip]

In the above example, it seems the Dole voters are insincerely truncating 
in order to create a circular tie.  If that is there strategy, then 
surely they would elect the 1/2 vote option, in order to win the tie.  
They would fail to do so only out of ignorance.  Whether they are 
truncating out of strategy, laziness, or sincere indifference, counting 
the one-half vote for tiebreak purposes would correspond to their true 
intentions, as it would elect their candidate.  Therefore, I think the 
example shows only that making the 1/2 vote optional could, in some 
cases, by the fortuity of the ignorance of insincere voters, result in 
the "true" Condorcet winner emerging from the tiebreak.

Consider a slight modification of this scenario: Dole's strategists get a 
minority of his supporters, 18 per cent of the total, to order-reverse 
(alternatively, they really prefer Nader), the rest sincerely vote Dole, 

28 Dole, Clinton
18 Dole, Nader
20 Clinton
34 Nader, Clinton 

Now we have a circular tie, and if no 1/2 votes are counted between Nader 
and Dole for the 20 Clinton voters, Nader is least-beaten with only 46 
against, though he lost by 12 to Dole, while Clinton lost by only 4 to 
Nader.  But if the half-votes are counted, Clinton is least beaten, with 
52 against to 54 and 56 against Dole and Nader.  No rational Clinton 
voter who understood the system would refrain from choosing the 1/2 vote 
option, but I suggest that few voters will ever understand the definition 
and significance of "least-beaten" under Condorcet, and that it is those 
voters who are sincerely indifferent who are most likely to fail to 
choose the 1/2 vote option through incomprehension or neglect.  So I 
think it should be made difficult to elect the "zero" option if its is 
allowed.  Perhaps the voter should have to give a rational explanation of 
why he would not want the 1/2 vote to count in case of a tiebreak, in 
order to opt out of it.

  -- Hugh Tobin

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