Defensive strategy criteria for voting systems
This is the letter that I said I'd send, about the defensive
strategy criteria for voting systems.
A majority has the power to gain any outcome that its members
all want. They can gain the election of any candidate they
want to, or gain the non-election of any candidate they want
to. But it's a question of what they have to do to gain that
With any method, with the possible exception of Borda, no
insincere strategy is needed to elect a candidate whom they
all want to elect. But if they all want to ensure the non-election
of some candidate, then it isn't so easy. With most voting systems,
some sort of insincere strategy is needed.
"Defensive strategy" is the term that refers to what the members
of a majority must do in order to gain a candidate's election
or non-election, when they all want that result.
This is important, because, in our political elections, we all
know that drastically insincere defensive strategy is routinely
used. People vote for a lesser-evil. They tell you that they're
going to "hold [their] nose and vote for Gore", not because they
like him, but only to defeat someone whom they rate as worse.
But the freedom to vote sincerely is important in Debian elections
too. You don't want a method that forces a majority to vote
incincerely to get a result that they want, be it the election
of an alternative or the non-election of an alternative. A majority
should be able to get its way without falsifying its preferences.
That's why the defensive strategy criteria are important.
Now I'd like to define the 5 defensive strategy criteria:
1. Strategy-Free Criterion (SFC):
Because SFC is about the freedom to sincerely vote all of one's
preferences, its first requirement is that the voting system
allow a voter to express as many prefernces as he/she wishes.
It's possible to allow that, for reasonable-size candidate sets,
with any implementation, but the method's definition should allow
that right even if a particular implementation limits the length
of a ranking.
SFC's 2nd requirement:
If no unfelt preferences are voted, and if a majority of all the
voters vote the Condorcet Winner over candidate B, then
candidate B shouldn't win.
definitions of terms used in that definition:
Condorcet winner: A candidate who, when compared to each one
of the others, is ranked over that other candidate by more voters
Alternatively, if "A beats B" means that more voters have ranked
A over B than vice-versa, then the Condorcet winner is the
candidate who'd beat each one of the others if everyone sincerely
ranked all of the candidates.
It goes without saying that if you rank A but you don't rank B,
that counts as ranking A over B.
Condorcet winner is often abbreviated "CW".
Voting an unfelt preference: That means voting X over Y, when
you prefer Y to X, or are indifferent between those 2 candidates.
SFC gets its name from the fact that, with complying methods,
the members of that majority who rank A over B don't have to
do anything else in order to ensure that B won't win. No one
has a need to do other than sincerely rank all of the candidates.
SFC is met by every Condorcet version (I'll demonstrate these
compliances in an immediately subsequent message). It isn't
met by any other methods.
Generalized SFC (GSFC):
The first requirement, of the freedom to express as many preferences
as one wishes to, is the same as in SFC.
If no unfelt preferences are voted, and if a certain member of
the sincere Smith set is voted over candidate B by a majority of
all the voters, and if B isn't in the sincere Smith set, then
B shouldn't win.
The Smith set is the smallest set of candidates such that every
candidate in the set beats every candidate outside the set.
The sincere Smith set is the Smith set that would exist if everone
sincerely ranked all of the candidates. It's a generalization of
the Condorcet winner to situations where there isn't a Condorcet
GSFC extends SFC to cases where there's no Condorcet winner.
When there isn't a Condorcet winner, there will still be a Smith
GSFC is met only by those Condorcet versions that only drop
a defeat if it's the weakest defeat in some cycle (SSD is included
among those methods, as I'll show in the next message).
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 can't win, without
any member of that majorit voting a less-liked candidate over
a more-liked one.
WDSC is met by all of the Condorcet versions, and by a number
of other good methods, including the simple method known as
Strong Defensive Strategy Criterion (SDSC):
Same as WDSC except that "...over a more-liked candidate" is
replaced by "...equal to or over a more-liked candidate".
SDSC is strictly met only by the Condorcet versions that only
drop a defeat if it's the weakest defeat in some cycle.
Stronger Defensive Strategy Criterion (SrDSC):
If a majority of all the voters prefere A to B, then they
should have a way of voting that will ensure that B won't win,
even if every member of that majority sincerely votes every
pairwise preference that he has, involving one or two candidates
whom he prefers to B.
Like SDSC, SrDSC is met only by those Condorcet versions that
only drop a defeat if it's the weakest defeat in some cycle.
Next I'll send demonstrations of compliance with these criteria.
That message will conclude this series of messages about better
circular tie solutions.
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