## A completely idiotic Instant Runoff Voting (IRV) election

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• Warren Smith posted (24 Aug 2010) a link to page discussing a simple IRV election: 18: A B C 24: B C A 15: C A B ... That verdict might be justified on
Message 1 of 6 , Sep 2, 2010
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Warren Smith posted (24 Aug 2010) a link to page discussing a simple IRV
election:

18: A>B>C
24: B>C>A
15: C>A>B

Quoting from the page:

> FAILURE OF THE SNIFF TEST: First of all, without any analysis at all,
> who do you think ought to win this election?
> It sure looks to me like B is the "most correct" and "most democratic"
> winner. But IRV elects A.

That verdict might be justified on positional grounds: B has both the
most first preferences and the most
second preferences and so looks the prettier winner.

But the objection is mostly based on ranking information which the IRV
voters were content to give because IRV meets
Later-no-Harm. If the A and B supporters are mostly concerned to
elect their favourites ( perhaps encouraged
by accurate pre-election first-preference polling) then with a method
that fails Later-no-Harm and meets Later-no-Help
(such as Bucklin or Range / Score) the cast ballots would more likely
look like:

18: A
24: B
15: C>A

Does A now look like the wrong winner?

> Score voting <http://rangevoting.org/RangeVoting.html> considers this
> election an easy call. It would elect B if all voters gave score X to
> their first choice, Y to their second,
> and Z to their third, for /any/ X?Y?Z, not all equal.

Really?

18: A9, B1, C0
24: B9, C1, A0
15: C9, A8, B0

A wins. Doesn't this example qualify?

Chris Benham

http://rangevoting.org/CompleteIdioticIRV.html

[Non-text portions of this message have been removed]
• ... this ... to ... No - you ve picked two different values for Y. Using any values for X, Y and Z satisfying Warren s constraints: A scores 18X + 15Y + 24Z B
Message 2 of 6 , Sep 2, 2010
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>> Score voting <http://rangevoting.org/RangeVoting.html> considers
this
>> election an easy call. It would elect B if all voters gave score X
to
>> their first choice, Y to their second,
>> and Z to their third, for /any/ X?Y?Z, not all equal.

>Really?

>18: A9, B1, C0
>24: B9, C1, A0
>15: C9, A8, B0

>A wins. Doesn't this example qualify?

No - you've picked two different values for Y.

Using any values for X, Y and Z satisfying Warren's constraints:

A scores 18X + 15Y + 24Z
B scores 24X + 18Y + 15Z
C scores 15X + 24Y + 18Z

B-A is therefore 6X + 3Y - 9Z; this is >0 for all values of X, Y, Z
satisfying the constraints.
B-C is 9X -6Y - 3Z; this is >0 for all values of X, Y, Z satisfying the
constraints.

--
Jack Rudd
• What does the phrase not all equal refer to then? Chris Benham
Message 3 of 6 , Sep 2, 2010
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What does the phrase "not all equal" refer to then?

Chris Benham

--- In RangeVoting@yahoogroups.com, jackkelshallrudd@... wrote:
>
> >> Score voting <http://rangevoting.org/RangeVoting.html> considers
> this
> >> election an easy call. It would elect B if all voters gave score X
> to
> >> their first choice, Y to their second,
> >> and Z to their third, for /any/ X?Y?Z, not all equal.
>
> >Really?
>
> >18: A9, B1, C0
> >24: B9, C1, A0
> >15: C9, A8, B0
>
> >A wins. Doesn't this example qualify?
>
> No - you've picked two different values for Y.
>
> Using any values for X, Y and Z satisfying Warren's constraints:
>
> A scores 18X + 15Y + 24Z
> B scores 24X + 18Y + 15Z
> C scores 15X + 24Y + 18Z
>
> B-A is therefore 6X + 3Y - 9Z; this is >0 for all values of X, Y, Z
> satisfying the constraints.
> B-C is 9X -6Y - 3Z; this is >0 for all values of X, Y, Z satisfying the
> constraints.
>
> --
> Jack Rudd
>
• To the values of X, Y, and Z (because then the election would be a three-way tie.) You use the SAME value of X, Y, and Z for every voter, but the values you
Message 4 of 6 , Sep 2, 2010
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To the values of X, Y, and Z (because then the election would be a
three-way tie.)

You use the SAME value of X, Y, and Z for every voter, but the values
you use must be "not all equal" to each other.

--
Dale Sheldon-Hess

On Thu, Sep 2, 2010 at 11:46 AM, cbenhamau <cbenhamau@...> wrote:
>
>
>
> What does the phrase "not all equal" refer to then?
>
> Chris Benham
>
> --- In RangeVoting@yahoogroups.com, jackkelshallrudd@... wrote:
> >
> > >> Score voting <http://rangevoting.org/RangeVoting.html> considers
> > this
> > >> election an easy call. It would elect B if all voters gave score X
> > to
> > >> their first choice, Y to their second,
> > >> and Z to their third, for /any/ X?Y?Z, not all equal.
> >
> > >Really?
> >
> > >18: A9, B1, C0
> > >24: B9, C1, A0
> > >15: C9, A8, B0
> >
> > >A wins. Doesn't this example qualify?
> >
> > No - you've picked two different values for Y.
> >
> > Using any values for X, Y and Z satisfying Warren's constraints:
> >
> > A scores 18X + 15Y + 24Z
> > B scores 24X + 18Y + 15Z
> > C scores 15X + 24Y + 18Z
> >
> > B-A is therefore 6X + 3Y - 9Z; this is >0 for all values of X, Y, Z
> > satisfying the constraints.
> > B-C is 9X -6Y - 3Z; this is >0 for all values of X, Y, Z satisfying the
> > constraints.
> >
> > --
> > Jack Rudd
> >
>
>
• ... Not all equal to each other. (If X = Y = Z, there s no way to meaningfully determine a winner.) -- Jack Rudd
Message 5 of 6 , Sep 2, 2010
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>What does the phrase "not all equal" refer to then?

Not all equal to each other. (If X = Y = Z, there's no way to
meaningfully determine a winner.)

--
Jack Rudd
• The not all equal problem was already covered (in both mailing lists). I wonder also what do words easy call mean. Score does not force all voters to use
Message 6 of 6 , Sep 2, 2010
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The "not all equal" problem was already covered (in both mailing lists).

I wonder also what do words "easy call" mean. Score does not force all
voters to use the same numeric values. If voters are free to use
whatever values they want (as in Score) then this election could give
whatever results, i.e. not an "easy call".

It would make more sense to say "Borda voting considers this election
an easy call" since in Borda the points that voters give are typically
fixed / tied to positions in the ballot. This rule works for all
weights that could be used in a Borda style method.

Juho

On Sep 2, 2010, at 10:46 PM, cbenhamau wrote:

>
> What does the phrase "not all equal" refer to then?
>
> Chris Benham
>
> --- In RangeVoting@yahoogroups.com, jackkelshallrudd@... wrote:
>>
>>>> Score voting <http://rangevoting.org/RangeVoting.html> considers
>> this
>>>> election an easy call. It would elect B if all voters gave score X
>> to
>>>> their first choice, Y to their second,
>>>> and Z to their third, for /any/ X?Y?Z, not all equal.
>>
>>> Really?
>>
>>> 18: A9, B1, C0
>>> 24: B9, C1, A0
>>> 15: C9, A8, B0
>>
>>> A wins. Doesn't this example qualify?
>>
>> No - you've picked two different values for Y.
>>
>> Using any values for X, Y and Z satisfying Warren's constraints:
>>
>> A scores 18X + 15Y + 24Z
>> B scores 24X + 18Y + 15Z
>> C scores 15X + 24Y + 18Z
>>
>> B-A is therefore 6X + 3Y - 9Z; this is >0 for all values of X, Y, Z
>> satisfying the constraints.
>> B-C is 9X -6Y - 3Z; this is >0 for all values of X, Y, Z satisfying
>> the
>> constraints.
>>
>> --
>> Jack Rudd
>>
>
>
>
>
> ------------------------------------
>