# [EM] I need an example of Condorcet method being subjected

Kathy Dopp kathy.dopp at gmail.com
Sat Jan 23 08:29:42 PST 2010

```Thanks again Kristofer for the explanations.  Terrific.

On Sat, Jan 23, 2010 at 10:41 AM,
<election-methods-request at lists.electorama.com> wrote:
> From: Kristofer Munsterhjelm <km-elmet at broadpark.no>
> To: kathy.dopp at gmail.com
>
> Kathy Dopp wrote:
>> Thanks Kristofer for the explanations.  Do you know a good place that
>> discusses the Ranked Pairs method of resolving cycles, or all the
>> methods of resolving cycles?  I would still like an example of  a
>> spoiler in Condorcet no matter how unlikely if possible.  Thank you.
>
> Wikipedia explains Ranked Pairs well enough:
> http://en.wikipedia.org/wiki/Ranked_Pairs
>
> It doesn't explain River, because that method is less known. In both
> Ranked Pairs and River, you first sort the majorities ("A beats B") by
> magnitude, greatest first.
> In Ranked Pairs, you then go down the list, "locking" majorities except
> if you lock "A beats B" and "B beats C", you can't lock "C beats A"),
> and at the end you have an ordering, and the candidate at the top of
> this ordering is the winner.
> In River, you do the same, except that you're also forbidden from
> locking a victory against someone who has already had a victory locked
> against him (e.g. "A beats B", then you can't lock "C beats B"). The
> root of the tree diagram (base of the river) is the winner.
>
> As for a spoiler in your terms, consider this very simple election
>
> 10: A>B>C
> 10: B>C>A
> 11: C>A>B
>
> If the method picks A, then B is a spoiler for C, because removing B
>
> 21: C>A
> 10: A>C
>
> If the method picks B, then C is a spoiler for A, because removing C
>
> 21: A>B
> 10: B>A
>
> If the method picks C, then A is a spoiler for B, because removing A
>
> 20: B>C
> 11: C>B.
>
> That should work for any election method that reduces to a majority vote
> when there are only two candidates, because, as I've shown, it doesn't
> matter which candidate is elected - you can still show there's a spoiler.
>

>> Maybe one should add also the requirement that the spoiler makes the
>> result worse from spoiler's or spoiler's supporters' point of view.
>
> Yes, although that cannot be mechanically tested. For some very strange
> methods, it might be true that adding a candidate changes the winner to
> someone who everybody who voted for the winner ranked ahead of him, but
> that would be a very strange method indeed.
>
>> Another possible modification is not to require f(X) to be high. One
>> would just see what would have happened with and without the spoiler.
>> According to that definition also strong candidates (but not actual
>> winners) could be spoilers. (Typically term spoiler refers to minor
>> candidates since these discussions typically refer to a two-party
>> set-up, but the corresponding scientific term might or might not be
>> limited to minor candidates and/or this particular set-up.)
>
> Then a spoiler is just a candidate whose presence shows IIA failure,
> subject to that this IIA failure must happen in first place (the winner
> changes, not lower in the ranking). The definition of IIA implies that
> the candidate ("spoiler") can't be the winner.
>
>
> From: Kristofer Munsterhjelm <km-elmet at broadpark.no>
> To: kathy.dopp at gmail.com

> As a note: some methods (most discussed here, actually) also permit both
> truncation and equal-ranking. If one takes that into account, the
> formulas become more complex still.
>
> Yet, on another level, this may not really matter. On the one hand, if

>From an election administration and public verifiability of the
outcomes point of view, the complexity always matters.

> there'll ever just be a few candidates, the amount of information to
> transmit is managable. On the other, setting a hard limit to, say, "no
> more than 5 candidates may participate in this election" is rather
> inelegant, and I would say, unfair, and if the potential number of
> candidates can grow to any number, it doesn't matter what formula is
> being used as long as it's superpolynomial (and so the values grow very
> large very quickly). Truncation or no truncation, equal rank or not, the
> number of unique orderings grow in that manner.
>
> From: Kristofer Munsterhjelm <km-elmet at broadpark.no>
> To: kathy.dopp at gmail.com
>>
>> Monotonicity is a mathematical concept that is fairly simple to
>> describe. There is non-decreasing monotonicity, strictly increasing
>> monotonicity, non-increasing monotonicity, etc.  Arrow describes the
>> concept re. elections fairly well in one of his fairness conditions.
>>
>> IRV/STV are the only alternative voting methods I am aware of that
>> fail this monotonicity condition that Arrow's fairness condition
>> requires but I have not studied all alternative methods so there must
>> be others that fail Arrow's monotonicity criteria.  Plurality
>> elections do *not* fail this criteria which is why IRV/STV fail more
>> of Arrow's fairness criteria than plurality does.
>>
>> The simplest way to state it in English is that the act of voting in
>> any one election should be monotonically increasing by giving the
>> voter the right to know that voting for a candidate always increases
>> that candidate's chances of winning holding all other things constant
>> (given the votes of other voters).  In other words, mathematically,
>> increasing the input or x value, always increases the output or y
>> value in a monotonically increasing function.
>
> That could be interpreted in two ways. Do you mean that a voter adding a
> ballot that ranks A above B should not cause A to lose to B, or that if

No, monotonicity does not require that condition, merely that the
voter increases the chances, rather than decreases the chances, of his
candidates' winning relative to other voters.

If one ranks a 2nd choice, in any voting method that finds compromise
candidates (not IRV/STV) that can cause a voter's 2nd choice, rather
than his first choice, to win.

> a ballot were replaced by one where A is moved further towards top rank,
> A shouldn't lose? Or both?
>

Kathy Dopp

Town of Colonie, NY 12304
phone 518-952-4030
cell 518-505-0220

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