Votes Against Tiebreaker

[Blake Cretney]

On Tue, 20 Oct 1998 04:57:11   New Democracy wrote:
>Greetings,
>
>     On Sat, 17 Oct 1998, MikeO wrote:  Here's the votes-against:
>
>A>B 40
>B>C 61
>C>A 51
>
>B wins by any of the VA methods, such as plain Condorcet(EM),
>Smith//Condorcet(EM), Schulze, or SD.
>
>Dear MikeO,
>
>     B  also wins by Plurality. This tiebreaker solution is the same as
>Plurality.

If you want to show something of this type, you have to provide the
initial ballots from which the VA scores can be calculated.  For
example
20 A B C
and so on.  Otherwise it is impossible to tell how many first choice
votes a candidate received.

Secondly, giving one example in which two methods behave the same
is not sufficient to prove they are equivalent.  Instead you must
provide a more general logical argument.  However, one case is
sufficient to show two methods are not equivalent.

40 A B C
35 B C A
15 C A B
10 C B A
   A  B  C
A  X  55 40
B  45 X  75
C  60 25 X

The winner in the Condorcet-type methods you mention is B.  The winner
by plurality is A.  There is no Condorcet Winner, so this is what you
would call a tie-breaking situation.

>     Does candidate B have a majority in his win?
>     If so, - where are the numbers that prove the majority?
>
>     Majority is defined as a number greater than one half of the total.
>     61 is not greater than one half of 152 (40+61+51).

I think that when we refer to a majority view, it should refer to the
support of some statement that voters can agree or disagree with.
For example:
	A majority say that C is acceptable
	A majority say that C is better than B
	A majority say that C is the best candidate
Do the phrases
	C is the majority choice
	C has a majority
	C wins by a majority
correspond to any majority held proposition, or any set of majority
held propositions?


>     If you say that 61 is a majority of 100, the number of votes, I will
>say 51 is also a majority of 100. And, we cannot have two majorities - the
>definition of majority rules out more than one majority.
My definition of a majority:

When the voters are allowed to express their opinion on some proposition,
and more than half of those expressing an opinion give the same answer,
this is a majority.

So, if more than half of those expressing an opinion say A is better
than B, then the statement "A is better than B" has the support of
a majority.  Clearly my definition does not rule out the idea of
conflicting majorities.

What is your definition of a majority?  I am hoping for something more
profound than "the winner at IRO".  Does your definition mean that
there is a majority who agree with any definite statement?  Does it
preclude conflicting majorities?

Blake



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