[EM] Criteria definitions

[MIKE OSSIPOFF]

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Stephane wrote:

Please explicite:

>FBC, SFC, GSFC, WDSC, & SDSC.

(.... Criteria)

If Mr. Ossipoff could provide a reference on a website with a definition
for each criteria

I reply:


The criteria are defined at http://www.electionmethods.org
at that website's technical evalulation page.

But let me define them here. There's been discussion of other
ways to define FBC, but the definition that I give here is the one
that I use, in my public advocacy. The other definitions suggested
are good too, but tend to be too complicated or wordy for public
use.


Favorite Betrayal Criterion (FBC):

By voting someone else over his/her favorite candidate, a voter
should never gain an outcome that s/he prefers to every other outcome
that the could get in that election without doing so.

[end of definition]

What this means is that a complying method never gives anyone incentive
to vote someone else over their favorite.

For the other definitions, let me define sincere voting:

A voter votes sincerely if he doesn't falsify a preference, or
fail to vote a sincere preference that the balloting system in use would
allow him to vote in addition to the preferences that he actually
does vote.

A voter votes a preference for X over Y if he prefers X to Y and
votes X over Y.

[end of definition]

A definition of voting X over Y:

A voter votes X over Y if he votes in a way so that it's possible to
devise a configuration of other voters' votes such that, if we delete from
the ballots all the candidates other than X & Y, X will be the unique
winner if & only if we count that voter's ballot.

[end of definition]

Other versions of this were proposed, and I liked some of the other
versions too. I might not remember all of the changes that were
suggested, but some of them sounded fine to me. Richard suggested
a number of changes, some of which I've incorporated or noted here.
It's possible that I've forgotten some of the suggested changes.

One proposal was:

A voter votes X over Y if he votes in such a way that if only his
ballot is counted, and we delete all the candidates from that ballot
except for X & Y, X wins.

[end of definition]

That 2nd definition is newer to me, and so I can't guarantee it
as well as I can guarantee the original one. It sounds good though.

It's been a while since these definitions were discussed, and there
may have been improving suggestions that I don't remember now.

Falsifying a preference means voting some X over some Y when one
doesn't prefer X to Y.

Strategy-Free Criterion (SFC):

If no one falsifies a preference, and if a majority of all the voters
prefer the sincere CW to candidate B, and vote sincerely, then
candidate B shouldn't win.

[end of definition]

Generalized Strategy-Free Criterion (GSFC):

If no one falsifies a preference, and if X is in the sincere Smith
set, and Y is not, and if a majority prefer X to Y and vote sincerely,
then Y shouldn't win.

[end of definition]

Weak Defensive Strategy Criterion (WDSC)

If a majority of all the voters prefer A to B, then they should
have a way of voting that will ensure that B won't win, without any
of them having to reverse a sincere preference.

[end of definition]

Strong Defensive Strategy Criterion (SDSC):

If a majority of all the voters prefer A to B, then they should
have a way of voting that will ensure that B won't win, without
any of them having to reverse a sincere preference or vote a less-liked
candidate equal to a candidate whom they've voted for.

[end of definition]


Stephane continues:

and if possible a counter-example for each of these
criteria that Ranked Pair is supposed to fail, I would be glad to read
it.

The only one of these criteria that Ranked-Pairs(wv) fails is
FBC. Ranked-Pairs(margins) fails all of them, as do all the margins
methods.

Here's an example:

Sincere preferences:

100: ABC
49:  BAC
75:  CBA

Suppose that no one falsifies a preference, and that the 49 B voters
and the 75 C voters vote sincerely, voting all of their preferences.
But suppose also that the 100 A voters truncate, by not ranking B.

Now B is beaten by C, with a margin of 26. B beats A, with a margin
of 49+75-100 = 24. A beats C, with a margin of 100+49-75 = 74.

A's defeat margin is the least, and A wins, contrary to what SFC
requires. Anything that fails SFC also fails GSFC, which is a generalization 
of SFC. If B is the sincere CW (and he is in this
example), then B is in the sincere Smith set and A is not.

Suppose the A voters order-reversed against B. There's a majority
who prefer B to A. Do they have a way of voting that will ensure
that A won't win? What if they truncate?

When the A voters order-reverse, the difference now is that
B's defeat by C has a margin of 100+75-49 = 126.

Say the B voters truncate by not ranking A. That means that now
A's defeat of C has a margin of 100-75 = 25.

So here are the defeat margins: C25, B126, and A24. A wins when
order-reversing, even if the B voters truncate.

If truncation won't keep A from winning, what will? Order reversal
will. Defensive order-reversal by the C voters. They can vote
B alone in 1st place, so that now 75+49 voters rank B over C, and
B remains voted CW.

But that majority has no way to keep A from winning without order-reversal.

Anyting that fails WDSC fails SDSC too, since SDSC merely ads
an additional requirement to WDSC.

So I've shown that the margins methods fail every one of those
criteria.

Mike Ossipoff







Maybe Mike already have, I am sorry the election-methods archive is too
huge...

>From my point of view, margins vs winning votes is a flase problem.
If you do not allow truncated list they should always bring the same
result.

Stéphane Rouillon



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