# [EM] Defeat strength, Winning Votes vs. Margins, what to do with equal-ranks on the ballot?

Kevin Venzke stepjak at yahoo.fr
Thu Jun 6 01:59:19 PDT 2019

```Hi Robert,

Le dimanche 2 juin 2019 à 02:10:13 UTC−5, robert bristow-johnson <rbj at audioimagination.com> a écrit :
>
>> Hi Robert,
>Hi,
>> I know that you feel it's adequate that there is a probabilistic relationship between (x-y) and (x+y).  I think
>> the relationship to expect in reality is unclear. Consider that in real world experience major contests that
>> involve the strongest candidates and most of the voters are often close races, in which case (x-y) doesn't
>> predict (x+y) well at all.
>
>it seems to me that one would expect x-y to scale with x+y.  if the decisiveness (which is the name that i give
>the percent margin, (x-y)/(x+y) ) is about the nature of the individuals voting, not about their quantity) is
>unchanged with size, then x-y is expected to get bigger as x+y does.  if the decisiveness is the equal between
>two paired runoffs in RP or Schulze, which decision is more important to satisfy?  the one involving more voters
>weighing in or the pairing with fewer?

And:

> > Personally I would say that (x-y) just reveals the lowest possible value for (x+y).
>No, i think that, if statistics are generated from actual elections you'll find (assuming x>y) that x-y will correlate
>with x+y.  The expectation value of x-y will increase with x+y .  I think viewing it as a binary probability distribution
>where the probability that a random voter votes for candidate X is x/(x+y) and the probability this randomly
>chosen voter votes for candidate Y is y/(x+y).  In this group I am leaving out the voters that preferred neither X nor Y.

Most candidates can't actually win, in a reasonable method, so their contests shouldn't be affecting the result (so asto minimize spoilers). So even if you are correct that (x-y) scales with (x+y) for most candidates, the situation wherewe need it to work is where (x+y) is high; whether it's true with unviable candidates shouldn't matter.

In the real world with two candidates there is an incentive to compete over the median voter, because the candidatewho can do that has the majority (or close). If the two candidates are nominated and campaign effectively then (x-y)should be small.

Possibly RCV in some form could change this dynamic, although that doesn't seem like it would be a good thing(i.e. higher margins between the most competitive candidates).
>  there are people disappointed with the result of any election.  the idea of majority rule is to reduce
>the number of disappointed persons with franchise.  assuming all voters have equal franchise, the net
>number of people being disappointed are the Winning votes minus Losing Votes.  If we want to minimize that,
>we emphasize the results of elections with larger margins over those of smaller margins.

I like the idea of measuring disappointment, but I think it has to be done per voter and based on what results themethod can actually offer. When X beats Y with some margin or vote count, we don't know much about what woulddisappoint X>Y voters or what their goals are. If Y is neither a voter's favorite nor least favorite, whether they wantY to be defeated depends on what else is on the table. If the method can only realistically elect Y or Z, thendisappointment from the resolution of X vs. Y will depend a lot on the opinions on Y vs. Z.
Kevin
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