[EM] Examples: Margins, strategy pushover
nkklrp at hotmail.com
Sat Apr 28 19:30:55 PDT 2001
Proponents of other voting systems always say that pairwise-count
methods are strategy-ridden. I'm going to show some examples here, to
show that they're right--when the method a Margins method.
Though I don't think the Condorcet Criterion is worth anything by
itself, most people here value it. So why not take it another step,
and consider how a sincere CW can lose, in a pairwise-count method.
Two things can defeat a sincere CW in a pairwise-count method:
Truncation, and falsification (which includes order-reversal).
Mere voting of an unfelt preference, as opposed to order-reversal,
can only do it if there's a great deal of indifference in the CW's
support. So usually I say that it's truncation & order-reversal that
can make a sincere CW lose.
One would think that would be of some interest to people who
think the sincere CW should win.
With wv, truncation can never steal the election from a well-supported
sincere CW. If a majority prefers the sincere CW to candidate B,
and if no one falsifies a preference, and if that majority vote sincerely,
then B can't win. That means too, of course, that truncation
by B voters can't make B win.
With wv, order-revesal by B voters can only succeed in taking victory
from a sincere CW if either the CW isn't supported against B, or if
the CW's voters co-operate with their own victimization by voting for
B. That's important: Order-reversal only works against people who
trust and help you, in wv.
As these examples will show, none of these things can be said for
In these examples there are 3 groups of voters, whose sincere preferences
are as follows:
In the examples I have numbers to the left of the rankings, representing the
numbers of people in each of the above preference groups. The
rankings that follow the numbers are the actual rankings that each
Example 1, truncation:
In Margins, though B is the sincere CW, A wins because the A voters
truncated against B. This could happen intentionally, strategically,
or it could happen merely because the A voters didn't bother voting
a 2nd choice. Either way, though, it takes victory away from the
sincere CW and gives it to A, the truncators' candidate.
There's nothing rare or atypical about this example. This is something
that Margins will be doing.
Example 2, order-reversal:
Notice that the B voters didn't participate in their own victimization
by voting for their victimizers' candidate, but the A voters still
stole the election from B by their order-reversal strategy.
Notice that B has about as much 1st choice support as A, and that
B is sincere CW.
Even if B is about as big as A, the A voters are
safe order-reversing as long as A is bigger than B, and the candidate
whom they're insincerely upranking is less than half as big as A.
And of course it's necessary that A pairbeats C.
One amusing thing is that Margins advocates like to say that
wv punishes truncation and that Margins doesn't. They've got it
backwards. WV doesn't punish truncation--it merely doesn't let truncation
steal the election. But, with Margins, truncation, in the form
of not ranking a middle candidate who is sincere CW, will sometimes
cause the victory of someone whom the truncators like less than that
CW. If it happened reliably it would deter truncation as an offensive
strategy. But, as with order-reversal, there are easy conditions
in which truncation is safe. My point here, however, is that in
Margins, but not in wv, in a 3-candidate election, truncation can
cause the sincere CW to lose to someone whom the truncators like less
than the sincere CW. It's Margins, not wv, that will make you regret
that you truncated your ranking.
Anyway, note that in these examples, the only way that the victims
of the offensive strategy can thwart it is for C to vote B equal to C
(defending against truncation) or to vote B over C (defending aginst
order-reversal), or for the B voters to revere their A>C preference.
Those needs for those degrees of defensive insincerity are what
SFC, GSFC, WDSC, & SDSC are about. The truncation example is
a failure example for SFC, GSFC, & SDSC. The order-reversal example
is a failure example for WDSC & SDSC. For Margins. I should say that
if we modify the truncation example so that the B voters sincerely vote
A in 2nd place, it becomes an SFC & GSFC failure example, since those
criteria stipulate sincere voting by the B>A majority.
I've shown here some ways that Margins avoidably lets a sincere CW
lose, and makes more extreme defensive strategies necessary to thwart
the truncation or order-reversal. These are also examples for why
the majority defensive strategy criteria are desirable.
Now, Rob LG, Richard, & Blake have claimed that wv has strategy
problems. Would they be so kind as to post examples showing how bad
are the consequences of those strategy "problems"?
What they won't show you is these easy instances of a sincere CW
losing because of truncation or order-reversal, or the
need for drastic insincerity to prevent it--that's just a Margins
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