# Votes Against Tiebreaker

Blake Cretney bcretney at my-dejanews.com
Tue Oct 20 12:38:02 PDT 1998

```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

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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