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
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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