Single Winner math basics

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Single Winner math basics

Craig Carey-2
It becomes necessary again to state single winner math basics.

A voter has a range of 100 percent approval to minus 100 percent disapproval
for each candidate in a single winner election ( a 200 percent range) (with
an additional possible unknown/ don't care vote for those candidates whom the
voter does not take the time or effort to learn about).

Thus, in an election with three candidates (X, Y and Z)--

Voter A could vote-
X 100
Y   99
Z   98

Voter B could vote-
X  -98
Y  -99
Z  -100

With plain Condorcet each voter would be voting relatively the same.

If above zero values are deemed approval and below zero (minus) values are
deemed disapproval in Approval Voting, then Voter A approves all three
candidates and Voter B disapproves all three candidates.

Unfortunately, as mentioned sometime ago, percentage values cannot be used
since there is one whole candidate being elected and not some positive or
negative percentage of him/her (accumulated somehow from all voters).

The potential of plain Condorcet for electing candidates with disapproval
votes (first choice or a later choice) is absolutely critical.

The extreme case would be if a majority of the voters each voted minus 98 as
their first choice for candidate X (or using second choices X wins all
candidate pairs using minus 98, minus 99 and/or minus 100 votes if all voters
ranked all candidates in some combination of minus 98, minus 99 and minus
100). With plain Condorcet, candidate X would be elected.

How many EM folks want zero to minus 100 percent disapproval votes to be used
to help elect anybody ?

Thus, there is the multiple same choices (MSC) remedy. Each voter may approve
one or more candidates for the office using multiple same choices (a voter
votes 0, 1, 2, 3, etc. for each candidate or leaves a blank by the
candidate).

A 0 or blank vote would be a disapproval vote. NOTA would be  shorthand for a
0 vote for all candidates.

Step. 1. Candidates with majority 0 votes plus blanks would lose.
 
Step. 2. If 2 or more other candidates remain, then Condorcet may be used as
a tie-breaker (assuming computer voting is available with a large number of
voters).

Question- Should a Condorcet winner (winning all pair matches or in a tie
breaker) be allowed to be elected with a plurality only (highly possible with
truncated voting) ?

Step 3. If no candidate gets elected, then have a new election or have the
majority rule P.R. legislative body appoint the officer.

Attention Condorcet fans- Step 1 is a safety valve addition to pure/plain
Condorcet.
Step 2 means voting 1, 2, etc. would be a vote in the 100 percent to 0
percent approval range.

For computer programmer folks- a 1, 2, etc. vote would each beat 0 or blank
in Condorcet pair comparisons. If a voter votes in MSC for two or more
candidates at the same level (such as voting 1 for two or more candidates),
then each candidate gets 1 vote in Condorcet pair comparisons (not zero or
0.5 vote).

Thus in the recent Hitler-Stalin-Middle examples, Step 1 would be computed
first (with possibly each candidate having a majority disapproval).

Note- The above technically also applies with any single transferrable vote
proportional representation system for legislative bodies. However, since it
is possible for each voter to elect a legislative body member in multi-member
districts or at large, the minus percentages of plain Condorcet are greatly
reduced and the 0 or blank make no sense (unless a majority 0/blank vote for
all candidates means that the legislative body is not elected).

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Equivalent proposals (reply to Demorep)

Craig Carey-2
[hidden email] writes:
>
> It becomes necessary again to state single winner math basics.

Or the basics of 1 person's standards.

But, standards aside, I realize now that we don't really disagree
on methods! Demorep's proposal, listed below, in numbered steps, is
equivalent to Steve's proposal to use Condorcet's method but include
the use of NOTB--provided that NOTB can only disqualify an alternative
by being ranked over it by a full majority. This isn't exactly the same
as Steve's proposal, but it's close. It's also quite close to Lucien's
proposal, which is to immediately disqualifly any alternative which
has been disapproved by a full majority, and do a Pairwise-Count
between the un-disqualified ones.

So there isn't major disagreement on methods.

But Demorep's ranking notation is too different from what we're all
used to, since he'd give the lowest numbers to his least liked alternatives,
and the highest numbers to his most-liked alternatives, where the rest
of us would give a 1 to our 1st choice, a 2 to our 2nd choice, etc.
No matter how far apart you rate your 1st & 2nd choices--even if your
1st choice is rated +97 & your 2nd choice is rated -35, then for the
purposes of the Condorcet count, you might as well have just labeled
them 1st choice & 2nd choice. Indicating 1st choice, 2nd choice, etc.
is much simpler for people. With that small change in notation,
Demorep's proposal is only slightly different from those other
ones.

>
> A voter has a range of 100 percent approval to minus 100 percent disapproval
> for each candidate in a single winner election ( a 200 percent range) (with
> an additional possible unknown/ don't care vote for those candidates whom the
> voter does not take the time or effort to learn about).
>
> Thus, in an election with three candidates (X, Y and Z)--
>
> Voter A could vote-
> X 100
> Y   99
> Z   98
>
> Voter B could vote-
> X  -98
> Y  -99
> Z  -100

In your system, the negative ratings would simply be counted as
disapprovals, correct? And then, after disqualifying the candidates
disapproved by full majority, we'd do a Condorcet count among the
rest, based on the voters' ordering of the candidates.

>
> With plain Condorcet each voter would be voting relatively the same.
>
> If above zero values are deemed approval and below zero (minus) values are
> deemed disapproval in Approval Voting, then Voter A approves all three
> candidates and Voter B disapproves all three candidates.
>
> Unfortunately, as mentioned sometime ago, percentage values cannot be used
> since there is one whole candidate being elected and not some positive or
> negative percentage of him/her (accumulated somehow from all voters).
>
> The potential of plain Condorcet for electing candidates with disapproval
> votes (first choice or a later choice) is absolutely critical.


This is dealt with by Lucien's & Steve's proposals, with which yours
is almost equivalent. But, you know, it isn't really a problem. If you
disapprove of someone, surely you'll rank other candidates over him.
If you completely disapprove him, you'll probably rank a number of
candidates over him. Ordinary Condorcet's method _does_ count majority
disapprovals. As you said, it counts relative disapprovals, but
what's the difference, if a candidate can't win because a full majority
have ranked someone else over him? As I said, Condorcet does a very
good job of rejecting majority-disapproved candidates.

Besides, a multicandidate single-winner election is really a
relative choice anyway. It's a choice of which candidate we want,
relative to the others. There's nothing wrong with a method that
goes by relative preferences & relative disapprovals. And, in
practice, it will reject the same majority-rejected candidates
that your method would, unless everyone is majority-rejected--
in which case it will elect one of them anyway. (But not with
Steve's, Lucien's & your modifications)

You know, when a good rank-balloting method like Condorcet is
used, there's going to be a good selection. There's no excuse
for any voter rejecting all the candidates, because any group
dissatisfied with the people planning to run could ask someone
they like to run also, something which, as Steve or Rob pointed
out, would be much more feasible with Condorcet than with Plurality.

So there's no reason why someone disapproved by a majority would
ever have to win. I claim that you're worrying needlessly about that,
because the selection will be too good for that to happen.

>
> The extreme case would be if a majority of the voters each voted minus 98 as
> their first choice for candidate X (or using second choices X wins all
> candidate pairs using minus 98, minus 99 and/or minus 100 votes if all voters
> ranked all candidates in some combination of minus 98, minus 99 and minus
> 100). With plain Condorcet, candidate X would be elected.
>
> How many EM folks want zero to minus 100 percent disapproval votes to be used
> to help elect anybody ?

It would serve people right for not running someone they can like. If
that negative-rated candidate is the best of the set that people
picked to run & organized candidacies for, then the public have merely
gotten what they asked for, by not taking enough interest to try to
run good candidates.

Besides, if negative ratings disqualified someone, how would we
ever elect Clinton?

>
> Thus, there is the multiple same choices (MSC) remedy. Each voter may approve
> one or more candidates for the office using multiple same choices (a voter
> votes 0, 1, 2, 3, etc. for each candidate or leaves a blank by the
> candidate).

I disagree only with the order in which you'd number the candidates,
and your name for the method. As I said, it would be much easier,
simpler, & more familiar for people to just rank 1st choice, 2nd
choice, etc. And either include NOTB in their ranking over candidates
they disapprove, or mark some candidates with a "D" for disapproval.
As for the name, what's wrong with "Condorcet with NOTB" or
"Condorcet with disapproval"? That's more descriptive.

>
> A 0 or blank vote would be a disapproval vote. NOTA would be  shorthand for a
> 0 vote for all candidates.
>
> Step. 1. Candidates with majority 0 votes plus blanks would lose.
>  
> Step. 2. If 2 or more other candidates remain, then Condorcet may be used as
> a tie-breaker (assuming computer voting is available with a large number of
> voters).
>
> Question- Should a Condorcet winner (winning all pair matches or in a tie
> breaker) be allowed to be elected with a plurality only (highly possible with
> truncated voting) ?

Sure. If the voters who needed the compromise didn't vote for him,
that's their fault--that they didn't vote a 2nd choice to avoid
the election of somoene worse.

>
> Step 3. If no candidate gets elected, then have a new election or have the
> majority rule P.R. legislative body appoint the officer.
>
> Attention Condorcet fans- Step 1 is a safety valve addition to pure/plain
> Condorcet.

Something that you, Lucien & Steve basically agree on. I don't object
to it, though I don't consider it necessary, given Condorcet's
defeat of majority-rejected candidates.

> Step 2 means voting 1, 2, etc. would be a vote in the 100 percent to 0
> percent approval range.
>
> For computer programmer folks- a 1, 2, etc. vote would each beat 0 or blank
> in Condorcet pair comparisons. If a voter votes in MSC for two or more
> candidates at the same level (such as voting 1 for two or more candidates),
> then each candidate gets 1 vote in Condorcet pair comparisons (not zero or
> 0.5 vote).
>
> Thus in the recent Hitler-Stalin-Middle examples, Step 1 would be computed
> first (with possibly each candidate having a majority disapproval).
>
> Note- The above technically also applies with any single transferrable vote
> proportional representation system for legislative bodies. However, since it
> is possible for each voter to elect a legislative body member in multi-member
> districts or at large, the minus percentages of plain Condorcet are greatly
> reduced and the 0 or blank make no sense (unless a majority 0/blank vote for
> all candidates means that the legislative body is not elected).
> .-
>


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