3 Apr 2011 08:16

### Help naming a new method

Hi all,

I have a new voting method and I think I need some help naming it.  Let me say, first of all, that I admit it may be too complicated for use by the general public.  It's a score aggregating method, like Score Voting.

Each voter scores each candidate on a scale of 0-100.  Each candidate's votes are aggregated independently, with their societal score given by finding the largest number, x, such that x percent of the voters gave that candidate a grade of x or higher.

So a candidate where 71% of the people gave a grade of 71 or higher (but the same can't be said of 71+epsilon) will get a final score of 71.

It shares a strategy-resistance property with the median that any voter whose score was above the societal score, if he were allowed to change his vote, could do nothing to raise the societal score.  (Also, a voter whose score was below the societal score could do nothing to lower the societal score.)  This means that if you're only grading one candidate (e.g. choosing an approval rating for the sitting president), then there is a strong incentive for everyone to submit an honest vote.

Of course, if there are multiple candidates then there will always be some instances where voters can benefit from voting dishonestly.  If we are entirely pessimistic and assume everyone is dishonest and gives fully extreme scores, then where the median would return an extreme score, this method does as good as approval voting or score voting.  That is, it returns the percentage of people who gave maximum grades.

It can be generalized to "find the largest number, x, such that F(x) percent of the voters gave the candidate a grade of x or higher," for a non-decreasing function F.   F(x)=50, for example, is basically equivalent to "find the median".  But anything more complicated than F(x)=x is probably hopeless for explaining to people.  And the diagonal function F(x)=x has some nice properties.  For example, one voter can never unilaterally move the output by more than 100/N, where N is the number of voters.

I thought of this method about three years ago.  I've been sitting on it since then, proving things for my doctoral thesis, which I finished last fall.  I did present this method at the Public Choice Society meeting about a year ago.  And I told Drs. Balinski and Laraki about it some time ago.  They make mention of it in their recently published book "Majority Judgment".

I'd like to publish some things in a journal, but I'm thinking I may need a better name for the method.  So far, I've called it "the linear median" and "the diagonal median".  I've considered "the consensus median" or "the consensus score", but that may be misleading, associating it with consensus societies.

Any ideas?

Balinski and Laraki call it "the linear median" in their book.  Is that good enough?

Jameson, in particular, has been concerned about careful naming in the past, so his input would be especially appreciated.

Thanks,

Andy Jennings

```----
Election-Methods mailing list - see http://electorama.com/em for list info
```
3 Apr 2011 13:08

### Re: Help naming a new method

```Andy Jennings wrote:

> Balinski and Laraki call it "the linear median" in their book.  Is that
> good enough?

I think linear median is good enough. Perhaps you'd want to clarify it
by calling it "the linear median method" or "linear median ratings".
----
Election-Methods mailing list - see http://electorama.com/em for list info

```
3 Apr 2011 13:13

### Re: new issue of Voting Matters

```Jeffrey O'Neill wrote:
> Hello,
>
> I just noticed that we have a new issue of voting matters and a new
> editor (Prof. Tideman), and I haven't seen a post on this on this list.
>
> Here is my blog post on the new issue: http://www.openstv.org/node/130
>
> And the issue itself: http://www.votingmatters.org.uk/ISSUE28/INDEX.HTM

That's interesting. Of course, since I've been looking for ways to
generalize divisor party list methods to multiwinner methods, that
particular paper drew most of my interest, though it does seem to be
quite complex. I'll consider it in greater detail when I get the time.
----
Election-Methods mailing list - see http://electorama.com/em for list info

```
3 Apr 2011 21:30

### Re: Help naming a new method

```Andy wrote:
> I have a new voting method and I think I need some help naming it.  Let
> me say, first of all, that I admit it may be too complicated for use by
> the general public.  It's a score aggregating method, like Score
> Voting.
>
> Each voter scores each candidate on a scale of 0-100.  Each candidate's
> votes are aggregated independently, with their societal score given by
> finding the largest number, x, such that x percent of the voters gave
> that candidate a grade of x or higher.
>
> So a candidate where 71% of the people gave a grade of 71 or higher
> (but the same can't be said of 71+epsilon) will get a final score of
> 71.
>
> It shares a strategy-resistance property with the median that any voter
> whose score was above the societal score, if he were allowed to change
> his vote, could do nothing to raise the societal score.  (Also, a voter
> whose score was below the societal score could do nothing to lower the
> societal score.)  This means that if you're only grading one candidate
> (e.g. choosing an approval rating for the sitting president), then
> there is a strong incentive for everyone to submit an honest vote.
>
> It can be generalized to "find the largest number, x, such that F(x)
> percent of the voters gave the candidate a grade of x or higher," for a
> non-decreasing function F.   F(x)=50, for example, is basically
> equivalent to "find the median".  But anything more complicated than
> F(x)=x is probably hopeless for explaining to people.  And the diagonal
> function F(x)=x has some nice properties.  For example, one voter can
> never unilaterally move the output by more than 100/N, where N is the
> number of voters.
>
> I thought of this method about three years ago.  I've been sitting on
> it since then, proving things for my doctoral thesis, which I finished
> last fall.  I did present this method at the Public Choice Society
> meeting about a year ago.  And I told Drs. Balinski and Laraki about it
> some time ago.  They make mention of it in their recently published
> book "Majority Judgment".
>
> I'd like to publish some things in a journal, but I'm thinking I may
> need a better name for the method.  So far, I've called it "the linear
> median" and "the diagonal median".  I've considered "the consensus
> median" or "the consensus score", but that may be misleading,
> associating it with consensus societies.

Hi Andy,

Please see chapter 3 of my dissertation:

http://www.cse.wustl.edu/~legrand/dissertation.pdf

It motivates and describes a rating system I call AAR DSV (Average-
Approval-Ratings Declared-Strategy Voting) that is equivalent to the
system applied to each candidate in your "linear median" method.  The
motivation is based on how rational voters would vote to try to pull the
outcome of a Average-based rating system as close to their ideal point as
possible.  The chapter also outlines a continuous range of rating systems
that includes both the standard AAR DSV and Median systems (including the
generalized ones you mention), interpolating between them using a two-
dimensional parameterization, and uses data from Metacritic.com to find
the "best" rating system in that range.  I prove that, if all voters are
only interested in moving the outcome as close to their ideal point as
possible, all of these systems are nonmanipulable.  This
nonmanipulability of course disappears when these systems are applied to
each candidate in a single-winner election.  My recent research has dealt
with generalizing these rating systems to higher-dimensional voting/
outcome spaces of various shapes; I haven't considered applying them to
electing a single winner from a discrete set of candidates in a while.

I presented a paper on AAR DSV called "Approval-rating systems that never
reward insincerity" at the 2nd International Workshop on Computational
Social Choice (COMSOC-2008):

http://www.csc.liv.ac.uk/~pwg/COMSOC-2008/

I'd like to see a copy of your doctoral thesis as well.

--
Rob LeGrand
rob <at> approvalvoting.org
----
Election-Methods mailing list - see http://electorama.com/em for list info

```
4 Apr 2011 01:50

### margins of victory with different voting methods

```http://rangevoting.org/ElMargins.html

--

--
Warren D. Smith
"endorse" as 1st step)
and
math.temple.edu/~wds/homepage/works.html
----
Election-Methods mailing list - see http://electorama.com/em for list info

```
4 Apr 2011 04:10

### Re: margins of victory with different voting methods

```An odd collection of elections to report on - I question whether they

US Electoral College - done with each state done separately, unlike
most any other election - meaning that various parts are done in
different ways.

Competition among Chirac, Le Pen, and Jospin in France in 2002.  Each
of them got around 5 million votes with the other dozen sharing around
15 million.

Since Jospin was third and the 15 million were unwilling to vote for
Le Pen, Chirac got millions more votes in the runoff.

Perhaps worth your reporting, but seems like the oddity deserves
mentioning.

Perhaps worth mentioning Plurality's weakness here - could have had a
different method that did not drop Jospin.

Dave Ketchum

On Apr 3, 2011, at 7:50 PM, Warren Smith wrote:

> http://rangevoting.org/ElMargins.html
>
> --
> Warren D. Smith
> "endorse" as 1st step)
> and
> math.temple.edu/~wds/homepage/works.html

----
Election-Methods mailing list - see http://electorama.com/em for list info

```
4 Apr 2011 04:52

### Re: margins of victory with different voting methods

```
On Apr 3, 2011, at 10:10 PM, Dave Ketchum wrote:

> US Electoral College - done with each state done separately, unlike
> most any other election - meaning that various parts are done in
> different ways.

but not to a significant degree.  *every* state, except Maine and
the plurality winner in that state.  Maine is 4 electoral votes,

the interesting thing is, that for the first time i know of, a state
(Nebraska) has actually split their slate of electors in 2008.
Nebraska was, essentially, a Red state (GOP, McCain), but the
congressional district around Omaha went to Obama.  so it was five
electoral votes split 4 and 1.

is there any historical case in modern American electoral history
where a state (having similar law as Nebraska or Maine) has, because
of the outcome, split their electoral vote?  i know of no other case.

for the most part, it's winner take all, which gives big states a big
swing vote (Ohio is the most reputed to having this quality making it
the quintessential "battleground state") and the small states (like
the one i grew up in and the one where i live now) get "compensated"
for their having less of a swing effect by having more electoral votes
per capita than the big states.  even so, prez candidates do not spend
any time during the General Election season in hardly any of the small
states like North Dakota or Vermont.

--

r b-j                  rbj <at> audioimagination.com

"Imagination is more important than knowledge."

----
Election-Methods mailing list - see http://electorama.com/em for list info

```
4 Apr 2011 21:15

### Re: margins of victory with different voting methods

``` > To: election-methods <election-methods <at> electorama.com>
>
> On Apr 3, 2011, at 10:10 PM, Dave Ketchum wrote:
>
>> US Electoral College - done with each state done separately, unlike
>> most any other election - meaning that various parts are done in
>> different ways.
>
> but not to a significant degree.  *every* state, except Maine and
> the plurality winner in that state.  Maine is 4 electoral votes,

Each state is done with *very* different ways in that they vary in:
1. who is allowed to vote - many states disenfranchise anyone who has
committed a prior felony, even after they've served their time and
done probation,

2. many states disenfranchise recent movers and students - anyone who
has not lived for at least 30 days at the same address or who does not
have  a local state driver's license, etc. and other states do not

3. whether or not votes cast in the wrong precinct are still counted
in state and federal elections, under what circumstances provisional
ballots are counted, how closely the signatures have to match or
not...

4. how strict the matching rules are that purge voters from the voter
rolls by matching with social security, driver's license, property
tax, and other databases (probably depends on the partisanship of the

5. the extent to which votes are open to fraudulent manipulation -
some states use e-ballots which are wide-open to undetectable vote
fraud, others use auditable voter marked paper ballots but count them
electronically and never audit them, some states do audits of some,
but not all of their ballots (neglecting to audit any mail in ballots
for instance) and no states audit sufficiently to prevent incorrect
outcomes in close contests

6. the extent to which the public is allowed access to electoral
records necessary to verify the integrity of the tallies (most states
are highly secretive and allow no public verification of ballot
security or jurisdiction-wide ballot and voter reconciliation,...

7. states vary widely in which private company they are allowing to

8. many states have already signed the popular vote compact, which I
believe is very unfortunate when states vary so widely in the public
verifiability of their election outcome accuracy and so many of them
are so hopelessly wide-open to undetectable vote tally manipulation
via vote manipulation, ballot box stuffing, ballot substitution,
ballot tampering, ballot absconding, failure to count ballots and the
like.

I agree with you that all states are currently winner-take-all in most
state and federal elections, except for NC's one judicial contest
which was IRV this year, but probably will never be again.  I think
the spate of IRV adoption is going to, unfortunately sour the public
on the idea of any more fair, auditable electoral methods due to its
many vagaries.

Regards,
--

Kathy Dopp
http://electionmathematics.org
Town of Colonie, NY 12304
"One of the best ways to keep any conversation civil is to support the
discussion with true facts."

Fundamentals of Verifiable Elections
http://kathydopp.com/wordpress/?p=174

Realities Mar Instant Runoff Voting
http://electionmathematics.org/ucvAnalysis/US/RCV-IRV/InstantRunoffVotingFlaws.pdf

View some of my research on my SSRN Author page:
http://ssrn.com/author=1451051
----
Election-Methods mailing list - see http://electorama.com/em for list info

```
14 Apr 2011 22:33

### basic fairness question

```Hello,

I apologize if I am asking a dumb question, but would appreciate any honest and practical advice from this
list. I am conducting an election among a group of colleagues who are all graduates of a fellowship
program. 45 people will vote on perhaps 30 candidates for roughly 15 seats.

The 45 are members of different classes from their fellowship. Group A (14 people) was in the fellowship for
18 months. Group B (12 people) overlapped with group A for a year, but all told were in the fellowship for 24
months. Group D (13 people) overlapped with Group B for a year, and were also in the fellowship 24 months.
Group C (6 people) started as members of Group B, and were asked to stay on for an extra year, finishing out
with Group D, for a total of 36 months in the fellowship.

The problem I am facing is a difference in name recognition between Groups A and D. Group C has the
distinction of having overlapped with everybody, and having spanned as much time in the fellowship as
both Groups B and D. So candidates from Group C are known best, and Group B is known by everyone, too. Group A
would seem to be at the worst disadvantage, since members of their group may have formed opinions of group D
simply by virtue of having paid attention to the fellowship after their own graduation, and this is
implausible in the reverse.

I could do an STV election for 15 seats. OR, I had been thinking of an electoral model for this group where we
didn't specify the number of seats available, and instead had voters rank their peers on a given set of
criteria. Set a threshold for election on this scale (say, 3.5 on a 5-point scale), and the candidates
whose average scores fall above that threshold are given a seat. In this case the candidates with lesser
name recognition, and therefore probably fewer "votes," would have an average score that is less precise
than those with greater name recognition, but it would still be a snapshot of how some number of voters feel
about them. Obviously there would have to be some minimum number of votes (or maybe evaluations is a better
term) on a candidate for it be considered a valid portr
ait of their fitness for election.

My question is, is this inherently unfair towards anyone from a statistical/electoral point of view? In
this particular situation, picking the number of seats beforehand is somewhat arbitrary--it is not a
given that it would have to be 15, though that is the number of candidates that would fall above an
"electable" threshold in my estimation.

Any advice, or fundamental concepts misunderstood by me?

Thanks very much.

Owen Dalby

----
Election-Methods mailing list - see http://electorama.com/em for list info

```
15 Apr 2011 03:34

### Re: basic fairness question

```At 04:33 PM 4/14/2011, Owen Dalby wrote:
>Hello,
>
>I apologize if I am asking a dumb question, but would appreciate any
>honest and practical advice from this list. I am conducting an
>election among a group of colleagues who are all graduates of a
>fellowship program. 45 people will vote on perhaps 30 candidates for
>roughly 15 seats.
>
>The 45 are members of different classes from their fellowship. Group
>A (14 people) was in the fellowship for 18 months. Group B (12
>people) overlapped with group A for a year, but all told were in the
>fellowship for 24 months. Group D (13 people) overlapped with Group
>B for a year, and were also in the fellowship 24 months. Group C (6
>people) started as members of Group B, and were asked to stay on for
>an extra year, finishing out with Group D, for a total of 36 months
>in the fellowship.
>
>The problem I am facing is a difference in name recognition between
>Groups A and D. Group C has the distinction of having overlapped
>with everybody, and having spanned as much time in the fellowship as
>both Groups B and D. So candidates from Group C are known best, and
>Group B is known by everyone, too. Group A would seem to be at the
>worst disadvantage, since members of their group may have formed
>opinions of group D simply by virtue of having paid attention to the
>fellowship after their own graduation, and this is implausible in the reverse.

You have not stated the purpose of the election. You are electing
"seats," but seats in what? Is the goal recognition of the
colleagues, or is it representation in a decision-making council?

>I could do an STV election for 15 seats. OR, I had been thinking of
>an electoral model for this group where we didn't specify the number
>of seats available, and instead had voters rank their peers on a
>given set of criteria. Set a threshold for election on this scale
>(say, 3.5 on a 5-point scale), and the candidates whose average
>scores fall above that threshold are given a seat. In this case the
>candidates with lesser name recognition, and therefore probably
>fewer "votes," would have an average score that is less precise than
>those with greater name recognition, but it would still be a
>snapshot of how some number of voters feel about them. Obviously
>there would have to be some minimum number of votes (or maybe
>evaluations is a better term) on a candidate for it be considered a
>valid portrait of their fitness for election.
>
>My question is, is this inherently unfair towards anyone from a
>statistical/electoral point of view? In this particular situation,
>picking the number of seats beforehand is somewhat arbitrary--it is
>not a given that it would have to be 15, though that is the number
>of candidates that would fall above an "electable" threshold in my estimation.
>
>Any advice, or fundamental concepts misunderstood by me?

Well, you haven't given us enough information. What are you doing?
There are "30 candidates" for "15 seats." Why are you holding an
election at all?

If the goal were representation, Asset Voting, which is a variant on
STV where exhausted ballots or extra ballots (above quota) can be
recast by those who received them, is about perfect. With this small
would meet and work out how to distribute the votes. There are
details that might not be obvious, such as quota (Hare or Droop, and
those who are accustomed to thinking of deterministic methods will go
for Droop, whereas those who see the value of encouraging compromise
will go for Hare, and allow those who refuse to compromise *to be
unrepresented*).

Otherwise what I'd suggest would be electing a "recognition
committee" -- use Asset! -- that is small enough to meet (in person
or by email) and decide things deliberatively, and let this committee
gather information, interview candidates and collect reports, etc.
(I.e., the "electorate" could be asked to rate candidates; the
committee can use this information flexibly.)

Asset voting is a device for boiling a group down to a smaller group
that fully -- or almost fully -- represents a larger group.

----
Election-Methods mailing list - see http://electorama.com/em for list info

```

Gmane