[EM] 02/06/02 - Adam's 02/02 example of three equal candidates:

[Richard Moore]

Donald Davison wrote:

> Now I would like to respond to your example of three candidates who are
> running neck and neck and tell how I think you should vote in four
> different election methods.

> 
> In the cases of the ABC methods, Approval, Borda, and Condorcet, you should
> only vote for your most favorite.  Let the other voters support your
> favorite with their lower choices while you will not be supporting their
> favorites.  This gives your favorite an advantage.

 >

> The success of your candidate will depend, in part, on the foolishness of
> the voters of the other candidates.  It will be foolish of them to give
> your candidate a vote besides voting for their candidate.  You are not to
> be that foolish, you are not to give any of their candidates a vote.   This
> is deception of course, but that is the design of the ABC methods.


Voters in Approval elections (and Borda and Condorcet elections) would do
well to ignore Donald's advice here. Depending on the folly of others is not
good strategy in these methods. Approval strategy is simple, but not as
simple as Donald believes it to be. (Actually, I've corrected him on this
before so I suspect that rather than believing this honestly, he is being
disingenuous.)

In Approval, with all three candidates running equal in the polls (as stated
in the premise, they are "neck and neck"), you have as much chance to be
instrumental in making your favorite win over your compromise as you do to
be instrumental in making your compromise defeat your least favorite. With
equal opportunities, which strategy do you choose: favorite only, or
favorite-plus-compromise? The answer can be found by looking at the cost of
guessing wrong. If you choose the first strategy, and it turns out to be
the wrong choice (meaning you end up either pushing your compromise to a
loss from a tie with your least favorite, with 50/50 odds the tie will
resolve to elect your least favorite, or you end up pushing your compromise
to a tie with your least favorite when otherwise your compromise would have
won), then the cost is the potential regret of causing your compromise lose
to your least favorite. Likewise, if you choose the second strategy, and
that strategy turns out to be the wrong choice, the cost is the equally
probable regret of causing your favorite lose to your compromise. Since
both strategies are equally likely to fail, the correct strategy is the
one which you would regret less in the event of failure. If your preference
for your favorite over your compromise is weaker than your preference for
your compromise over your least favorite, then vote for your top two.
Otherwise, vote for your favorite only.

The reason I think Donald is disingenuously promoting a lousy strategy
here is that, if he can convince people that his strategy really is
optimal, he can then argue that Approval is strategically equivalent to
Plurality.


> You must understand that in the ABC methods, the lower preferences are not
> back-up choices, they are votes that are counted at the same time as your
> first preference.


This is a non sequitur. Why is it that a choice cannot be a back-up choice
if it is counted at the same time as a first preference? It certainly cannot
be a back-up choice if it is not counted at all, as happens often in IRV.

 -- Richard