Discussion:
[EM] A Question about Pages 22-29/58 of Chapter 12 of Fobes' 'Ending the Hidden Unfairness of U.S. Elections
steve bosworth
2015-09-13 19:22:07 UTC
Permalink
Hi Richard,
Unfortunately, my other obligations have
not allowed me to reply to your answers to our 20th VoteFair/APR dialogue
until today. However, before I do so, I
would very much appreciate it if you would clarify a question that I have about
your book, ‘Ending the Hidden Unfairness of U.S. Elections’. With regard to pages 22 to 29/58 of Chapter
12, I finally understand how you arrived at the ‘score’ of 400 for the winning
sequence i.e. Elliot(E)>Selden(S)>Meredith(M)>Roland(R):

You started by adding up the number of
the 100 voters who had preferred each of the three candidates to the left of R,
over R, i.e. 60+70+70 = 200. You then
added the number who preferred those to the left of M, over M, i.e. 70+70=140. Next you added the number who preferred E
over S, i.e. 60. The sum of these 3
totals is 400, i.e. the largest score for any one of all the possible
sequences.

However, please also explain why the following simpler set of
calculations would not also always allow us to discover the most popular
sequence:



Firstly, find the grand total of preferences given by the 100
voters to each of all the candidates (4 in this example) over each of the
other candidates (3 in this example). The result is:

Elliot 200

Selden 180

Meredith 90

Roland 80



At least in this case, the same sequence is produced: Elliot 1st, Selden 2nd,
Meredith 3rd, and Roland 4th.

Why do we also have to calculate the score for each possible sequence?



What do you think?

Steve



Re: (21) APR: Steve's 20th dialogue
with Richard Fobes



>
From: election-methods-***@lists.electorama.com

> Subject: Election-Methods Digest, Vol 134, Issue 1

> To: election-***@lists.electorama.com

> Date: Sat, 1 Aug 2015 12:02:14 -0700

>

>> 1. Re: (20) APR: Steve's 20th dialogue with Richard Fobes

> (Richard Fobes)

>

>

> ----------------------------------------------------------------------

>

> Message: 1

> Date: Fri, 31 Jul 2015 17:07:34 -0700

> From: Richard Fobes <***@VoteFair.org>

> To: "election-***@lists.electorama.com"

> <election-***@lists.electorama.com>

el
VoteFair
2015-09-17 18:44:23 UTC
Permalink
On 9/13/2015 12:22 PM, steve bosworth wrote:
> ...
> [...] please [...] explain why the following simpler set of
> calculations would not also always allow us to discover the most
> popular sequence:
>
> Firstly, find the grand total of preferences given by the 100 voters to
> each of all the candidates (4 in this example) over each of the other
> candidates (3 in this example). The result is:
> Elliot 200
> Selden 180
> Meredith 90
> Roland 80
>
> At least in this case, the same sequence is produced:
> Elliot 1st, Selden 2nd, Meredith 3rd, and Roland 4th.

Yes, sometimes -- in SOME situations -- a simpler calculation (such as
this one) can identify the same winner and even the same ranking.

However, typically a shortcut fails to provide fair results in ALL
situations.

Consider that plurality (first-past-the-post) voting is a shortcut that
mistakenly assumes that the candidate with the most first-choice votes
is always the most popular. This shortcut does not work if the
candidate with the most first-choice votes does not ALSO get a majority
of (more than half) the votes.

In a similar way, instant-runoff voting is a shortcut that does work in
some situations. It is based on the shortcut of (mistakenly) assuming
that the candidate with the fewest first-choice votes is least popular.

Also in a similar way, your APR method will work in some situations.
Yet it too puts too much emphasis on first-choice votes without
considering secondary preferences (or somewhat-equal preferences for
those who prefer approval voting).

In contrast to methods that work SOME of the time, full fairness
requires that a method must produce fair results either ALL the time
(which is mathematically impossible if all fairness criteria are
considered), or MOST of the time. In the best methods, unfairness
(according to any fairness criteria) is rare. To get this level of
fairness, the voting method must look beyond the first-choice counts.

Back before computers became available, mathematical shortcuts were
often useful in some situations. Now, both in terms of calculation time
and the work of coding software, it's easier to do full calculations
using a fully-fair algorithm, compared to writing code that handles both
the shortcut and all the needed validity checking and related decision
handling (to handle the cases where the validity checks fail).

I hope this information helps not only you/Steve, but also helps some
other participants in this forum.

Richard Fobes

BTW, page numbers in an ebook reader do not match the page numbers in a
different ebook reader, and do not match the page numbers in a printed
edition.


On 9/13/2015 12:22 PM, steve bosworth wrote:
> Hi Richard,
>
> Unfortunately, my other obligations have not allowed me to reply to your
> answers to our 20^th VoteFair/APR dialogue until today.However, before I
> do so, I would very much appreciate it if you would clarify a question
> that I have about your book, ‘Ending the Hidden Unfairness of U.S.
> Elections’.With regard to pages 22 to 29/58 of Chapter 12, I finally
> understand how you arrived at the ‘score’ of 400 for the winning
> sequence i.e. Elliot(E)>Selden(S)>Meredith(M)>Roland(R):
>
> You started by adding up the number of the 100 voters who had preferred
> each of the three candidates to the left of R, over R, i.e. 60+70+70 =
> 200.You then added the number who preferred those to the left of M, over
> M, i.e. 70+70=140.Next you added the number who preferred E over S, i.e.
> 60.The sum of these 3 totals is 400, i.e. the largest score for any one
> of all the possible sequences.
>
> However, please also explain why the following simpler set of
> calculations would not also always allow us to discover the most popular
> sequence:
>
> Firstly, find the grand total of preferences given by the 100 voters to
> each of all the candidates (4 in this example) over each of the other
> candidates (3 in this example). The result is:
> Elliot 200
> Selden 180
> Meredith 90
> Roland 80
>
> At least in this case, the same sequence is produced: Elliot 1st, Selden
> 2nd, Meredith 3rd, and Roland 4th.
>
> Why do we also have to calculate the score for each possible sequence?
>
> What do you think?
>
> Steve
----
Election-Methods mailing list - see http://electorama.com/em for
steve bosworth
2015-09-17 22:13:36 UTC
Permalink
> Date: Thu, 17 Sep 2015 11:44:23 -0700
> From: ***@VoteFair.org
> To: election-***@electorama.com
> CC: ***@hotmail.com
> Subject: Re: A Question about Pages 22-29/58 of Chapter 12 of Fobes' 'Ending the Hidden Unfairness of U.S. Elections
Hi Richard ( and everyone else), Later I want to continue our dialogue compare VoteFair and APR for electing multiple winners, but now, please let me focus only on your explanation below about 'VoteFair popularity scoring' for electing single-winners and the need not to rely on shortcuts: S: As you may recall, I currently favor your VoteFair popularity ranking method for electing single-winners -- presidents, governors, majors, etc. It has the virtue of discovering the most popular candidate by counting all the preferences of all the voters and without eliminating any candidate until the most popular one has been discovered. It seems simpler and better than any other method that I have read about, including those I've seen discussed in EM. Still, I would like to receive any criticisms from anyone of this method for this purpose, or any arguments that prefer a competing method. Richard, I think your method would be even more appealing if it were safe to score its results by the 'shortcut' I asked about. It would be more appealing because more people would be able to understand exactly how it works, as well as it requiring a much simpler computer program. I understand that 'shortcuts' in general can be dangerous and that the particular ones you mention below with regard to 'plurality' and 'IRV' are flawed by the reason you give, i.e. their mistaken assumptions which motivate them. However, I am not yet aware that VoteFair popularity ranking makes any mistaken assumptions. Therefore, it currently still seems to me that simply counting the number of times each candidate is preferred over every other candidate would not be an unreliable 'shortcut' because would always enable us to discover the most popular candidate, as well as give use the whole correct sequence. Is there specific reason why I am mistaken in this view?Steve >
> On 9/13/2015 12:22 PM, steve bosworth wrote:
> > ...
> > [...] please [...] explain why the following simpler set of
> > calculations would not also always allow us to discover the most
> > popular sequence:
> >
> > Firstly, find the grand total of preferences given by the 100 voters to
> > each of all the candidates (4 in this example) over each of the other
> > candidates (3 in this example). The result is:
> > Elliot 200
> > Selden 180
> > Meredith 90
> > Roland 80
> >
> > At least in this case, the same sequence is produced:
> > Elliot 1st, Selden 2nd, Meredith 3rd, and Roland 4th.
>
> Yes, sometimes -- in SOME situations -- a simpler calculation (such as
> this one) can identify the same winner and even the same ranking.
>
> However, typically a shortcut fails to provide fair results in ALL
> situations.
>
> Consider that plurality (first-past-the-post) voting is a shortcut that
> mistakenly assumes that the candidate with the most first-choice votes
> is always the most popular. This shortcut does not work if the
> candidate with the most first-choice votes does not ALSO get a majority
> of (more than half) the votes.
>
> In a similar way, instant-runoff voting is a shortcut that does work in
> some situations. It is based on the shortcut of (mistakenly) assuming
> that the candidate with the fewest first-choice votes is least popular.
>
> Also in a similar way, your APR method will work in some situations.
> Yet it too puts too much emphasis on first-choice votes without
> considering secondary preferences (or somewhat-equal preferences for
> those who prefer approval voting).
>
> In contrast to methods that work SOME of the time, full fairness
> requires that a method must produce fair results either ALL the time
> (which is mathematically impossible if all fairness criteria are
> considered), or MOST of the time. In the best methods, unfairness
> (according to any fairness criteria) is rare. To get this level of
> fairness, the voting method must look beyond the first-choice counts.
>
> Back before computers became available, mathematical shortcuts were
> often useful in some situations. Now, both in terms of calculation time
> and the work of coding software, it's easier to do full calculations
> using a fully-fair algorithm, compared to writing code that handles both
> the shortcut and all the needed validity checking and related decision
> handling (to handle the cases where the validity checks fail).
>
> I hope this information helps not only you/Steve, but also helps some
> other participants in this forum.
>
> Richard Fobes
>
> BTW, page numbers in an ebook reader do not match the page numbers in a
> different ebook reader, and do not match the page numbers in a printed
> edition.
>
Kristofer Munsterhjelm
2015-09-18 19:53:32 UTC
Permalink
On 09/18/2015 12:13 AM, steve bosworth wrote:
>> Date: Thu, 17 Sep 2015 11:44:23 -0700
>> From: ***@VoteFair.org
>> To: election-***@electorama.com
>> CC: ***@hotmail.com
>> Subject: Re: A Question about Pages 22-29/58 of Chapter 12 of Fobes' 'Ending the Hidden Unfairness of U.S. Elections
>
> Hi Richard ( and everyone else),
>
> Later I want to continue our dialogue compare VoteFair and APR for
> electing multiple winners, but now, please let me focus only on your
> explanation below about 'VoteFair popularity scoring' for electing
> single-winners and the need not to rely on shortcuts:
>
> S: As you may recall, I currently favor your VoteFair popularity
> ranking method for electing single-winners -- presidents, governors,
> majors, etc. It has the virtue of discovering the most popular
> candidate by counting all the preferences of all the voters and without
> eliminating any candidate until the most popular one has been
> discovered. It seems simpler and better than any other method that I
> have read about, including those I've seen discussed in EM. Still, I
> would like to receive any criticisms from anyone of this method for this
> purpose, or any arguments that prefer a competing method.
>
> Richard, I think your method would be even more appealing if it were
> safe to score its results by the 'shortcut' I asked about. It would be
> more appealing because more people would be able to understand exactly
> how it works, as well as it requiring a much simpler computer program.
>
> I understand that 'shortcuts' in general can be dangerous and that the
> particular ones you mention below with regard to 'plurality' and 'IRV'
> are flawed by the reason you give, i.e. their mistaken assumptions which
> motivate them.
>
> However, I am not yet aware that VoteFair popularity ranking makes any
> mistaken assumptions. Therefore, it currently still seems to me that
> simply counting the number of times each candidate is preferred over
> every other candidate would not be an unreliable 'shortcut' because
> would always enable us to discover the most popular candidate, as well
> as give use the whole correct sequence. Is there specific reason why I
> am mistaken in this view?

That shortcut sounds like a variant of the "sum of defeats" method
mentioned here:
http://miroirs.ironie.org/condorcet/condorcet.org/emr/methods.shtml. The
variety would be in that the shortcut uses sum of victories rather than
sum of defeats, and on what it sums (in Condorcet terms, sounds more
like pairwise opposition than WV).

That page states that the sum-of-defeats method is not cloneproof and is
vulnerable to vote-splitting. That means that similarly aligned
candidates can sometimes hurt one another. I'd suspect that
sum-of-victories would also be vulnerable to cloning. E.g. suppose party
X would like to increase the score of their main candidate X1; they
could then introduce another candidate (say X2) and tell party
supporters to rank X1>X2>others. If I'm wrong about the shortcut being
sum-of-victories, do let me know, of course.

If you'd like a simple yet good Condorcet method, how about Ranked
Pairs/MAM[1]? It works like this:

1. Sort all the pairwise contests in order of strongest to weakest.
Discard those that are weaker than a majority.
2. Go down the list and lock in a pairwise contest unless it contradicts
a contest you locked in earlier[2].
3. Once you're done, reassemble the pairwise contests into a ranking.
The candidate that is ranked first on it wins.

Some additional details are required for breaking ties, but I've left
those out here.

-

[1] River is somewhat better, but its additional clause might sound
strange. It doesn't provide a social ordering either, just a winner.

[2] E.g. if you lock in A>B that means that A will be ranked higher than
B in the outcome. If you've locked in A>B and B>C, you can't lock in C>A
later on because that would put C above A, which would contradict A>B>C.
----
Election-Methods mailing list - see http://electorama.com/em for list info
VoteFair
2015-10-06 00:50:30 UTC
Permalink
As I'm working my way through messages, I see that this message answers
some questions I just asked in my reply to Steve. (I saw this message
awhile ago, but too long ago to remember it.)

Thank you Kristofer for your info and insights.

Richard Fobes

On 9/18/2015 12:53 PM, Kristofer Munsterhjelm wrote:
> On 09/18/2015 12:13 AM, steve bosworth wrote:
>>> Date: Thu, 17 Sep 2015 11:44:23 -0700
>>> From: ***@VoteFair.org
>>> To: election-***@electorama.com
>>> CC: ***@hotmail.com
>>> Subject: Re: A Question about Pages 22-29/58 of Chapter 12 of Fobes'
>>> 'Ending the Hidden Unfairness of U.S. Elections
>>
>> Hi Richard ( and everyone else),
>>
>> Later I want to continue our dialogue compare VoteFair and APR for
>> electing multiple winners, but now, please let me focus only on your
>> explanation below about 'VoteFair popularity scoring' for electing
>> single-winners and the need not to rely on shortcuts:
>>
>> S: As you may recall, I currently favor your VoteFair popularity
>> ranking method for electing single-winners -- presidents, governors,
>> majors, etc. It has the virtue of discovering the most popular
>> candidate by counting all the preferences of all the voters and without
>> eliminating any candidate until the most popular one has been
>> discovered. It seems simpler and better than any other method that I
>> have read about, including those I've seen discussed in EM. Still, I
>> would like to receive any criticisms from anyone of this method for this
>> purpose, or any arguments that prefer a competing method.
>>
>> Richard, I think your method would be even more appealing if it were
>> safe to score its results by the 'shortcut' I asked about. It would be
>> more appealing because more people would be able to understand exactly
>> how it works, as well as it requiring a much simpler computer program.
>>
>> I understand that 'shortcuts' in general can be dangerous and that the
>> particular ones you mention below with regard to 'plurality' and 'IRV'
>> are flawed by the reason you give, i.e. their mistaken assumptions which
>> motivate them.
>>
>> However, I am not yet aware that VoteFair popularity ranking makes any
>> mistaken assumptions. Therefore, it currently still seems to me that
>> simply counting the number of times each candidate is preferred over
>> every other candidate would not be an unreliable 'shortcut' because
>> would always enable us to discover the most popular candidate, as well
>> as give use the whole correct sequence. Is there specific reason why I
>> am mistaken in this view?
>
> That shortcut sounds like a variant of the "sum of defeats" method
> mentioned here:
> http://miroirs.ironie.org/condorcet/condorcet.org/emr/methods.shtml. The
> variety would be in that the shortcut uses sum of victories rather than
> sum of defeats, and on what it sums (in Condorcet terms, sounds more
> like pairwise opposition than WV).
>
> That page states that the sum-of-defeats method is not cloneproof and is
> vulnerable to vote-splitting. That means that similarly aligned
> candidates can sometimes hurt one another. I'd suspect that
> sum-of-victories would also be vulnerable to cloning. E.g. suppose party
> X would like to increase the score of their main candidate X1; they
> could then introduce another candidate (say X2) and tell party
> supporters to rank X1>X2>others. If I'm wrong about the shortcut being
> sum-of-victories, do let me know, of course.
>
> If you'd like a simple yet good Condorcet method, how about Ranked
> Pairs/MAM[1]? It works like this:
>
> 1. Sort all the pairwise contests in order of strongest to weakest.
> Discard those that are weaker than a majority.
> 2. Go down the list and lock in a pairwise contest unless it contradicts
> a contest you locked in earlier[2].
> 3. Once you're done, reassemble the pairwise contests into a ranking.
> The candidate that is ranked first on it wins.
>
> Some additional details are required for breaking ties, but I've left
> those out here.
>
> -
>
> [1] River is somewhat better, but its additional clause might sound
> strange. It doesn't provide a social ordering either, just a winner.
>
> [2] E.g. if you lock in A>B that means that A will be ranked higher than
> B in the outcome. If you've locked in A>B and B>C, you can't lock in C>A
> later on because that would put C above A, which would contradict A>B>C.

----
Election-Methods mailing list - see http://electorama.com/em for list info
VoteFair
2015-10-06 00:46:55 UTC
Permalink
Steve, you are suggesting a possibly new single-winner method. As I
understand it, you are suggesting the use of pairwise counting, putting
those pairwise counts into a (tally) table, and calculating a score for
each candidate, where the score is the sum of associated pairwise counts.

I do not know if this method has a name. Does anyone else know?

This method is certainly superior to plurality counting ("first past the
post"). It is probably superior to instant-runoff voting.

I'll let the supporters of approval voting voice their opinion about
whether this method is better or worse than approval voting.

However, the only advantage it has over the various Condorcet methods is
that it can be easily calculated using paper and pen.

The disadvantages of this method can be summed up by saying that it
would fail many fairness criteria. In other words, if it were added to
the comparison table in the Wikipedia "voting systems" page, then it
would not appear to be a good choice as a voting method.

You suggest that this method might be a "shortcut" for VoteFair
popularity ranking (which is mathematically equivalent to the
Condorcet-Kemeny method). But it is not a shortcut to any kind of
voting. It is a completely different method.

For your benefit, and for the benefit of anyone else who is learning
about voting methods, pairwise counting can be thought of as the first
step in the process of calculating the Condorcet-Kemeny,
Condorcet-Schulze/Beatpath, Ranked Pairs, and other Condorcet methods.
These different methods use the pairwise counts in different ways.
Steve, your new suggested method uses the pairwise counts in yet another
way.

You have speculated that your suggested method would "always" produce
the same results as VoteFair popularity ranking. As I tried to explain
before, that is not the case.

I looked for an example in which your method produces different results
compared to VoteFair popularity ranking. I did not find any specific
example, yet if I had lots of time I could fabricate such an example.

The reason I know that the two methods produce different results is that
I use "your" kind of calculation for some of the graphical bars that
appear in the results that are calculated at my VoteFair.org website,
and I have seen cases where the graphical bars do not consistently
lengthen with higher rankings. Those cases are uncommon, but they occur.

Specifically, if you look at the American Idol page on the VoteFair
website you will see results that have a column labeled "VoteFair
ranking score," and there are many links on that page that lead to other
computed results that show the same graphical-scoring column. This
"score" (which I could not find a better name for) is not used in any
aspect of VoteFair ranking. I created these horizontal bars in order
for them to be visually compared to the horizontal bars that indicate
plurality results. In all the American Idol results that I recently
looked at, the graphical bars consistently progress from shorter to
longer as the ranking priority increases. For those cases, your
suggested method and VoteFair popularity ranking do produce the same
ranking results (and, by extension, the same "winner").

Yet I have seen cases where these horizontal bars do not progress in
this typical pattern. In other words, VoteFair popularity ranking
produces a ranking that would be different compared to your suggested
method of just summing pairwise counts for each candidate.

Such atypical ("non-typical") cases tend to occur when a relatively few
number of ballots have been cast. As more ballots are cast, those
atypical patterns disappear.

What this means is that your suggested method might be useful in
situations where lots of people are voting, and where the pairwise
counting can be done on a computer, but where voters do not want to rely
on a computer for the final calculation step.

Someone else on this forum might be familiar enough with this method to
quickly identify which fairness criteria this method passes, and which
ones it fails.

I suspect that it fails the Condorcet criterion, which is a serious
weakness for a method that cannot be "hand counted." (Pairwise counting
by hand is tedious and error-prone.)

If you want to promote this method to voters as an improvement over
plurality voting and instant-runoff voting, please do so!

Perhaps such usage will be like training wheels on a bicycle, where
those extra wheels provide a comfortable halfway point between not
riding a bicycle and riding a bicycle. But just as training wheels need
to be taken off before someone can really ride a bicycle, this method is
not useful as an end result because there are multiple better
vote-counting methods.

Now that you are better understanding how to improve vote counting, I
also encourage you to apply this understanding to improve the counting
methods you propose in your APR method.

I apologize for the long delay (weeks!) in replying to your message.
Thanks for being interested in my feedback. I hope it's helpful.

Richard Fobes

On 9/17/2015 3:13 PM, steve bosworth wrote:
>> Date: Thu, 17 Sep 2015 11:44:23 -0700
>> From: ***@VoteFair.org
>> To: election-***@electorama.com
>> CC: ***@hotmail.com
>> Subject: Re: A Question about Pages 22-29/58 of Chapter 12 of Fobes'
> 'Ending the Hidden Unfairness of U.S. Elections
>
> Hi Richard ( and everyone else),
>
> Later I want to continue our dialogue compare VoteFair and APR for
> electing multiple winners, but now, please let me focus only on your
> explanation below about 'VoteFair popularity scoring' for electing
> single-winners and the need not to rely on shortcuts:
>
> S: As you may recall, I currently favor your VoteFair popularity ranking
> method for electing single-winners -- presidents, governors, majors,
> etc. It has the virtue of discovering the most popular candidate by
> counting all the preferences of all the voters and without eliminating
> any candidate until the most popular one has been discovered. It seems
> simpler and better than any other method that I have read about,
> including those I've seen discussed in EM. Still, I would like to
> receive any criticisms from anyone of this method for this purpose, or
> any arguments that prefer a competing method.
>
> Richard, I think your method would be even more appealing if it were
> safe to score its results by the 'shortcut' I asked about. It would be
> more appealing because more people would be able to understand exactly
> how it works, as well as it requiring a much simpler computer program.
>
> I understand that 'shortcuts' in general can be dangerous and that the
> particular ones you mention below with regard to 'plurality' and 'IRV'
> are flawed by the reason you give, i.e. their mistaken assumptions which
> motivate them.
>
> However, I am not yet aware that VoteFair popularity ranking makes any
> mistaken assumptions. Therefore, it currently still seems to me that
> simply counting the number of times each candidate is preferred over
> every other candidate would not be an unreliable 'shortcut' because
> would always enable us to discover the most popular candidate, as well
> as give use the whole correct sequence. Is there specific reason why I
> am mistaken in this view?
>
> Steve
>
> >
> > On 9/13/2015 12:22 PM, steve bosworth wrote:
> > > ...
> > > [...] please [...] explain why the following simpler set of
> > > calculations would not also always allow us to discover the most
> > > popular sequence:
> > >
> > > Firstly, find the grand total of preferences given by the 100 voters to
> > > each of all the candidates (4 in this example) over each of the other
> > > candidates (3 in this example). The result is:
> > > Elliot 200
> > > Selden 180
> > > Meredith 90
> > > Roland 80
> > >
> > > At least in this case, the same sequence is produced:
> > > Elliot 1st, Selden 2nd, Meredith 3rd, and Roland 4th.
> >
> > Yes, sometimes -- in SOME situations -- a simpler calculation (such as
> > this one) can identify the same winner and even the same ranking.
> >
> > However, typically a shortcut fails to provide fair results in ALL
> > situations.
> >
> > Consider that plurality (first-past-the-post) voting is a shortcut that
> > mistakenly assumes that the candidate with the most first-choice votes
> > is always the most popular. This shortcut does not work if the
> > candidate with the most first-choice votes does not ALSO get a majority
> > of (more than half) the votes.
> >
> > In a similar way, instant-runoff voting is a shortcut that does work in
> > some situations. It is based on the shortcut of (mistakenly) assuming
> > that the candidate with the fewest first-choice votes is least popular.
> >
> > Also in a similar way, your APR method will work in some situations.
> > Yet it too puts too much emphasis on first-choice votes without
> > considering secondary preferences (or somewhat-equal preferences for
> > those who prefer approval voting).
> >
> > In contrast to methods that work SOME of the time, full fairness
> > requires that a method must produce fair results either ALL the time
> > (which is mathematically impossible if all fairness criteria are
> > considered), or MOST of the time. In the best methods, unfairness
> > (according to any fairness criteria) is rare. To get this level of
> > fairness, the voting method must look beyond the first-choice counts.
> >
> > Back before computers became available, mathematical shortcuts were
> > often useful in some situations. Now, both in terms of calculation time
> > and the work of coding software, it's easier to do full calculations
> > using a fully-fair algorithm, compared to writing code that handles both
> > the shortcut and all the needed validity checking and related decision
> > handling (to handle the cases where the validity checks fail).
> >
> > I hope this information helps not only you/Steve, but also helps some
> > other participants in this forum.
> >
> > Richard Fobes
> >
> > BTW, page numbers in an ebook reader do not match the page numbers in a
> > different ebook reader, and do not match the page numbers in a printed
> > edition.
> >
>
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