[EM] Electowiki, Symmetrical ICT

[Michael Ossipoff]

== SYMMETRICAL ICT: ==


After this description and definition of Symmetrical ICT, I'll say a
few words of what it implies for the compatibility of FBC and
Condorcet's Criterion.

ICT stands for "Improved-Condorcet-Top". The idea for Improved
Condorcet is from Kevin Venzke. Improved Condorcet meets FBC. Then,
later, Chris Benham proposed completion by top-count, to achieve
"defection-resistance", avoidance of the Chicken Dilemma. Chris had a
long name for his method, but I called it "Improved-Condorcet-Top", in
keeping with Kevin's naming.

I later proposed that the Improved Condorcet improvement be done at
bottom-end as well, to almost achieve compliance with Later-No-Help,
which would achieve additional easing and simplification of strategy
need.

But the big improvements were those of Kevin and Chris.

I called my version Symmetrical ICT.

'''Symmetrical ICT:'''

(X>Y) means the number of ballots ranking X over Y
(Y>X) means the number of ballots ranking Y over X.
(X=Y)T means the number of ballots ranking X and Y in 1st place.
(X=Y)B means the number of ballots ranking X and Y at bottom
....(not ranking X or Y over anything)

iff means "if and only if".

X beats Y iff (X>Y) + (X=Y)B > (Y>X) + (X=Y)T

...except that two candidates can't beat eachother. If, by the above
beat-condition formula, two candidates beat eachother, then only one
of them beats the other. The one that beats the other is the one who is ranked
over the other on more ballots than vice-versa.


1. If one candidate beats everyone else, then s/he wins.

2. If everyone or no one is unbeaten, then the winner is the candidate
ranked in 1st place on the most ballots.

3. If some, but not all, candidates are unbeaten, then the winner is
the unbeaten candidate ranked in 1st place on the most ballots.

[end of definition of Symmetrical ICT]

'''Justification of Imroved Condorcet:'''

One justification is that it gains compliance with FBC.

It automatically avoids the chicken dilemma.

Additionally, it respects the preferencds, intent and wishes of
equal-top-ranking voters:

Suppose that you rank two candidates, X and Y in 1st place. You rank
them in 1st place because you'd prefer that they win, instead of the
other candidates.

Now, suppose that candidate X would beat everyone, and thereby win,
except that then you (and a few other people) move Y up to 1st place
too. Previously X beat Y. But now, because you people have moved Y to
1st place with X, you've removed some X>Y votes, and so now Y beats X.
And now, instead of someone beating everyone, there's a top-cycle in
which Z (the worst candidate) is a member. And, by whatever circular
tiebreaker is used, Z wins.

Did you want that to happen? When you ranked X and Y in 1st place, did
you mean that you wanted your last choice to win? No, you primarily
wanted X or Y to win. Well then, what if, for the purpose of the X/Y
pairwise comparison, you could cast a custom-made, adjustable, vote to
achieve the result that you prefer, to protect the win of someone in
{X,Y}. You don't want X or Y to beat eachother, because, as seen
above, that could make neither of them win, and give the win to
someone much worse. So you'd use that vote for the purpose of voting
against either candidate beating the other. For instance, if Y would
otherwise beat X, then you'd cast an X>Y vote, your vote against one
beating the other.

So then, what if we say that, when ranking X and Y in 1st place, in
addition to counting as pairwise votes for them over everyone else, it
also counts as a vote, by you, against either beating the other. That
would be the way to interpret your equal top ranking in a way that is
consistent with your interest, preferences, intent and wishes.

That's Improved Condorcet.

Now, traditionally, for the purpose of the Condorcet Criterion, we say
that X beats Y iff more people rank X over Y than Y over X. But, as I
said, the above-described Improved Condorcet interpretation of equal
top ranking is the interpretation that is more in keeping with the
interest, preferences, intent and wishes of the voter who votes that
equal top ranking. In other words, it has more legimacy than the
traditional interpretation, and the traditional definition of "beats",
quoted at the beginning of this paragraph.

And, since it has more legitimacy, it would be a better choice, when
deciding who beats whom, for the purpose of the Condorcet Criterion.

And when that interpretation and counting of equal top rankings is
used for the purpose of the Condorcet Criterion, Improved-Condorcet
meets Condorcet's Criterion.

Before someone says, "Yeah, you make Improved-Condorcet meet the
Condorcet Criterion by modifying Condorcet's Criterion to match
Improved Condorcet. But note that I told why the Improved Condorcet
interpretation of equal top ranking is more in keeping with the
interest, prefereces, intent and wishes of the equal top ranking
voter, and therefore is more legitimate. It'a a matter of using a more
legitimate interpretation, rather than just modifying a criterion to
match a method. Besides, the reason why the method uses that
interpretation is because it's more legitimate, and what the equal top
ranking voter prefers.

So: Improved Condorcet versions, including ICT and Symmetrical ICT,
meet the Condorcet Criterion, when it is defined more legitmately.

Likewise, then, it can be said that FBC and the Condorcet Criterion
are compatible, contrary to popular belief.

Though FBC is defined at its own eletowiki article, let me define it here too:

'''Favorite-Betrayal-Criterion (FBC):'''

A candidate is top-voted and at top on a ballot if that ballot doesn't
vote anyone over him/her.

If no one wins who isn't top-voted on your ballot, and then you move
an additional candidate to top, then that shouldn't cause to win any
candidate who isn't then at top on your ballotl

[end of FBC definition]

'''A few properties and criterion-compliances of Symmetrical ICT:'''

1. FBC

2. Automatically avoids chicken dilemma

3. Merely not ranking two unacceptable candidates, you're doing all
that can be done to make at least one of them beaten.

That simplifies bottom-end strategy. In traditional Condorcet, there
is strategic need to rank unacceptable candidates in reverse order of
winnability.


Michael Ossipoff