Single Vote in Multi-Winner Elections

[Brian Langstraat]

Most ballots in Iowa have fairly simple instructions.

For single-winner elections, the instructions are "Vote for no more than One".

For multi-winner elections (example of 4 winners), the instructions are "Vote for no more than Four".

These instructions could produce results with problematic issues such as:

Single-winner elections with non-majority plurality, and

Multi-winner elections with winner-takes-all by the majority.

Perhaps, the simplest change to these instructions that could reduce the problematic issues would be to essentially switch the instructions for single-winner and multi-winner elections.

For single-winner elections, the instructions are "Vote for any number".  (Approval Voting)

For multi-winner elections, the instructions are "Vote for no more than One".  (Single Vote)

The winners would be the candidate(s) with the most votes.

Approval Voting in single-winner elections seems like an obvious improvement.

Single Vote in multi-winner elections seems like a less obvious improvement.

Single Vote in Multi-Winner Elections would tend to elect more diverse representation while increasing the spoiler effect, since similar candidates would be likely to split votes.

Is there another name for "Single Vote in Multi-Winner Elections"?

Has research been done on this voting system?

[Kevin Baas]

The instructions should be:

For single-winner elections, the instructions are "Vote for as many as you like".

For multi-winner elections (example of 4 winners), the instructions are "Vote for as many as you like".

winner-take-all by the majority only happens when you don't properly eliminate ballots that are used to elect someone. (e.g. "bloc-voting" or non-normalized score-voting without surplus transfer)

subtracting the quota and transfering surplus is essential for having proportional multi-member elections.

any system that doesn't do that is FUBAR - is WORSE than our current, gerrymander-enabling system.

As for the single-winner case, that illustrates the flip-side of transfer: eliminated candidates should have their deficit votes transferred proportionally, until a single candidate has unanimous consent.

[Kevin Baas]

"Is there another name for "Single Vote in Multi-Winner Elections"?"

I'll hold my tongue...

"Has research been done on this voting system?"

Yes,  In my head, 5 seconds ago.  To summarize the conclusions: it sucks.

I have, earlier, done actually automated simulation of a number of other methods under an number of different scenarios.

The results and the code are available here:

http://autoredistrict.org/SI_simulation.zip

Tested under 4 different scenarios:

* everyone within a "party" (coalition) rates all candidates for their party the same, the party runs as many candidates as there are seats

* within a "party" (coalition), the candidates have a different popularity, linearly increasing (e.g. for 3 candidates, 1:2:3), the party runs as many candidates as there are seats

* everyone within a "party" (coalition) rates all candidates for their party the same, the party runs twice as many candidates as are expected to win

* within a "party" (coalition), the candidates have a different popularity, linearly increasing (e.g. for 3 candidates, 1:2:3), the party runs twice as many candidates as are expected to win

Tested under - if i recall correctly - something like 8 different vote shares between the two party.

Then equivalent ballots for different election system:

* score voting

* allocation voting

* ranked choice voting

* approval voting (approve as many or few as you like)

* approval voting (approve exactly X candidates. ("N Votes"))

Then additionally each of these systems were testing under two different versions:

* Non-transferable votes (e.g. block voting)

* Transferable votes (e.g. STV voting)

Making in total an apples-to-apples comparison of 5x2=10 different systems, under 2x2x8 = 32 different scenarios, for a total of 320 election simulated.

The primary conclusions (the two things that stand out like a sore thumb) are:

1) non-transferable vote systems are a DISASTER (this includes non-normalized score voting w/out proportional transfer)

2) STV w/Hare quota has marginally more proportional results for candidates with little support.

Note, that is going to be part of the "Supplementary Information" for an article that is going to be published very soon (probably next issue) in the journal "Political Insight".

Again, the full source code is available in that .zip file, so that if you don't believe me, you can check my work and even reproduce yourself, or run your own scenarios.

On Wednesday, February 22, 2017 at 12:41:07 PM UTC-6, Brian Langstraat wrote:

[Kevin Baas]

oh geez, i used 0.05 increments for the vote share, so 20 steps.  So 5x2=10 different systems, under 2x2x20 = 80 different scenarios, for a total of 800 election simulated.

[Brian Langstraat]

Kevin,

I appreciate your replies to my original posts.  

I am not claiming that "Single Vote in Multi-Winner Elections" would be the best possible voting system for multi-winner elections, but that it may be the simplest change to multi-winner elections that would reduce the chances of winner-takes-all by the majority.  

I agree that voting systems that transfer votes (such as Single Transferable Voting) and reweigh votes (such as Reweighted Approval Voting) are better, but they are also more complex since they require substantial redesign of ballots and/or counting votes in ways that could be confusing to voters.

The results of "Single Vote in Multi-Winner Elections" would usually be more proportional than gerrymandered districts which also has the problematic issue of winner-takes-all by the majority.  Additionally, the diverse committees should tend to resist partisan gerrymandering.  By the way, Iowa probably has one of the best systems for avoiding gerrymandering in the United States.

I have taken a look at your simulation results, but I do not have access to JAVA.

How many total candidates were simulated in each scenario?

Obviously, non-transferable votes had worse results than transferable votes.  However, "ntv allocation" seemed to do well in some of the scenarios.

Could allocation or n-votes be modified so only one vote is allowed?

I suspect that sharp changes with the simulated non-transferable voting is partially caused by the "winner-takes-all by the majority".

I think that this would be a worthwhile simulation include in the "Political Insight" article, at least as a baseline.

On Wednesday, February 22, 2017 at 1:31:42 PM UTC-6, Kevin Baas wrote:

[Kevin Baas]

"I agree that voting systems that transfer votes (such as Single Transferable Voting) and reweigh votes (such as Reweighted Approval Voting) are better,"

Okay, firstly, i'm not just saying they're better.  I'm saying if you DON'T do it, the result is WORSE than simple single-winner plurality.  So it's not even a choice.  It's mandatory.

"but they are also more complex since they require substantial redesign of ballots"

Not at all.

" and/or counting votes in ways that could be confusing to voters."

Voters don't count the votes.  Algorithms do.  Algorithms can't be confused.

Voters don't need to know the details of the algorithm.  They just need to know that it obeys later-no-harm.  That's all they need to know to properly fill out a ballot.

Besides, the point is moot.   There's no choice.  You HAVE to use a transferable vote system.  Otherwise the result is going to be even LESS proportional than single-winner plurality.

[Kevin Baas]

"I have taken a look at your simulation results, but I do not have access to JAVA."

Yes you do.  It's free on oracle's website.  

You can run it from the command line (on windows just start menu->run->type "cmd" and hit enter), "java -cp [classpath] [main class]".  in this case, you'd go to the folder you put it in and type:

java -cp . whicheverFileIsTheMainClassIForget.class

Also the source code is plain text, and you can download a Development environment for free on the web - Eclipse.

"How many total candidates were simulated in each scenario?"

Read the word .doc that's in the .zip file.  I misstated all the runs I did.  Also all the different systems I tested.  But it's stated correctly in the word doc.  I ran each scenario for everything from 1 to 8 candidates.

"Obviously, non-transferable votes had worse results than transferable votes.  However, "ntv allocation" seemed to do well in some of the scenarios."

In SOME scenarios,  a few.  And far worse than just running single-winner elections would do.

"Could allocation or n-votes be modified so only one vote is allowed?"

Yes, and they'd both be the same thing.  But why would you do that?

"I suspect that sharp changes with the simulated non-transferable voting is partially caused by the "winner-takes-all by the majority"."

It is COMPLETELY caused by that.  Because votes aren't transferred.

[Brian Langstraat]

Kevin,

I am not sure why you are assuming that "Single Vote in Multi-Winner Elections" would have worse results than single-winner plurality.  Have you simulated this before or point me to other research?

A simple example seems to have fairer results:

In 2 districts, both districts have a 55% vote for the Democratic candidate and a 45% vote for the Republican candidate.  Thus, 2 Democratic representatives are elected and winner-takes-all.

In 2 combined district, each party nominates a single candidate with a  55% vote for the Democratic candidate and a 45% vote for the Republican candidate.  Thus, 1 Democratic representative and 1 Republican representative are elected which is close to proportional.

The typical American voter (people in this group are exceptions) will have a hard time trusting "weird" looking ballots and "mysterious" algorithms.  Voter confusion/distrust and entrenched partisan politicians are the main reasons voting reform has been so unsuccessful.

[Kevin Baas]

"In 2 districts, both districts have a 55% vote for the Democratic candidate and a 45% vote for the Republican candidate.  Thus, 2 Democratic representatives are elected and winner-takes-all."

This is not a realistic scenario.  Districts tend to vary significantly in their demographic composition.  That's why state congress composition tends to be pretty proportional to the state popular vote, despite being elected by single-winner plurality.

"In 2 combined district, each party nominates a single candidate with a  55% vote for the Democratic candidate and a 45% vote for the Republican candidate.  Thus, 1 Democratic representative and 1 Republican representative are elected which is close to proportional."

Try this one out: In 2 combined district, each party nominates a single candidate with a  90% vote for the Democratic candidate and a 10% vote for the Republican candidate.  Thus, 1 Democratic representative and 1 Republican representative are elected which is NOWHERE close to proportional."

[Kevin Baas]

"The typical American voter (people in this group are exceptions) will have a hard time trusting "weird" looking ballots and "mysterious" algorithms.  Voter confusion/distrust and entrenched partisan politicians are the main reasons voting reform has been so unsuccessful."

I'd rephrase that: "Entrenched partisan politicians IS the main reasons voting reform hasn't happened. "

In places were voting reform has happened, for instance, almost everywhere there is a democracy except America, and some places in america, the citizens have been very happy with it and not at all confused.

We know this from surveys and what not.  It's empirical.

[Brian Langstraat]

A common name for "Single Vote in Multi-Winner Elections" is Single Non-Transferable Vote (SNTV).

Good descriptions for SNTV can be found at https://en.wikipedia.org/wiki/Single_non-transferable_vote and

 The Single Non-Transferable Vote (SNTV).

I have not been able to get the JAVA code working yet.  I have done most of my programming in MATLAB.

Adding a SNTV simulation to your SI_simulation code should be fairly simple and would be worthwhile to note in your "Political Insight" article since SNTV is mentioned related academic articles such as http://procaccia.info/papers/multi.ijcai07.pdf.  If the SNTV has worse results than single-winner plurality elections, then we can confirm your assumption.

I suspect that sharp changes with the simulated non-transferable voting is partially caused by the "winner-takes-all by the majority".

It is COMPLETELY caused by that.  Because votes aren't transferred.

My suspicion is that the simulations for the non-transferable voting systems are allowing majorities with multiple votes to overwhelm minorities.  Perhaps, only allowing single votes would reduce the majority dominance and allow smoother plot changes near the target.

[Kevin Baas]

"I have not been able to get the JAVA code working yet."

I just realized, you only have the sources, not the compiled class files.  You could still presumably compile it from the command line via javac, but I'd recommend installing an editor (an IDE, such as Eclipse or NetBeans) instead, and launching it from there.

It's really of no value if you can't edit the code, because all it will do from the command line is produce the spreadsheet you already have.

"Adding a SNTV simulation to your SI_simulation code should be fairly simple "

Simpler than you think.  Just add a "1" to the number of votes per ballot inputs.

" and would be worthwhile to note in your "Political Insight" article "

'tis past that stage.

"then we can confirm your assumption"

Not an assumption.  A deduction.  Part of which I explained to you already.

"My suspicion is that the simulations for the non-transferable voting systems are allowing majorities with multiple votes to overwhelm minorities."

Nope.  Quite the opposite: The problem is that a ballot is not removed after it is used to meet a quota.  Thus it gets used twice.  So the people voting for the majority actually get multiple votes, instead of just 1.  Meanwhile the ones that vote for a minority never get their vote used to meet a quota even once.

The golden rule of counting -- count each element exactly once -- is violated.

"Perhaps, only allowing single votes would reduce the majority dominance and allow smoother plot changes near the target."

Nope, the problem remains and is in fact even worse - because since the voter only expressed 1 choice, it is no longer even possible to transfer surplus votes - they just get thrown out.  Not only is the golden rule of counting violated, but there's now no longer any way to fix it.

Consider 4 winners, party 1 runs 3 candidates, party 2 runs 3 candidates.  The voters are evenly split.

However, Party 1 has a favorite, Party 2 nobody likes any of them, so they just vote randomly for their party.  there are 99 voters for each party.

Party 1 voters vote: 99 0 0 on party 1 candidates, and 0 0 0 on party 2 candidates.

Party 2 voters vote: 0 0 0 on party 1 candidates, and 33 33 33 on party 2 candidates.

Round 1: 99 0 0 33 33 33, candidate 1 for party 1 wins.  all votes for that candidate are eliminated.  Since there are no alternative choices expressed, the surplus votes cannot be transferred. Even though theoretically 1/4 of the vote should be counted as used, a full 1/2 are.

Round 2: 0 0 0 33 33 33, candidate 1 for party 2 wins, despite only receiving 1/6th of the total votes.   Again, no transfers.  Even though theoretically 1/4 of the vote should be counted as used, only 1/6th are.

Round 3: 0 0 0 0 33 33, candidate 2 for party 2 wins, despite only receiving 1/6th of the total votes.   Again, no transfers.  Even though theoretically 1/4 of the vote should be counted as used, only 1/6th are.

Round 4: 0 0 0 0 0 33, candidate 3 for party 2 wins, despite only receiving 1/6th of the total votes.   Again, no transfers.  Even though theoretically 1/4 of the vote should be counted as used, only 1/6th are.

Final result: party 1: 1 seat, party 2: 3 seats.  Despite the voters being split 1:1.

This is not an "assumption".

[Brian Langstraat]

"In 2 districts, both districts have a 55% vote for the Democratic candidate and a 45% vote for the Republican candidate.  Thus, 2 Democratic representatives are elected and winner-takes-all."

This is not a realistic scenario.  Districts tend to vary significantly in their demographic composition.  That's why state congress composition tends to be pretty proportional to the state popular vote, despite being elected by single-winner plurality.

Of course I was using 55% vs. 45% for simplicity.  I could use 58% vs. 42% and 52% vs. 48% with the same results (assuming same district size).  Districts do vary in their demographic composition, but gerrymandering has created plenty of near 55%/45% districts (close but likely to win) with some 20%/80% districts (packing opposition votes).  State congress composition tends to be pretty disproportional to the state popular vote due to gerrymandering and single-winner plurality. For example, Wyoming went about 65% R and 25% D for president and their single at-large representative, but their combined state congress was about 85% R and 15% D. http://www.nytimes.com/elections/results/wyoming

Try this one out: In 2 combined district, each party nominates a single candidate with a  90% vote for the Democratic candidate and a 10% vote for the Republican candidate.  Thus, 1 Democratic representative and 1 Republican representative are elected which is NOWHERE close to proportional."

A 90%/10% split is rare.  Only a few of the most partisan countles in the United States had that big of a split such as 90%/5% in Harding County, South Dakota. http://www.nytimes.com/elections/results/south-dakota

If SNTV was used and a single party was that dominant, then parties would run multiple candidates or third parties/ independents would run.  So a 60% D vs. 30% D vs. 10% R could occur with a result of 2 Democratic representatives.

[Brian Langstraat]

Voter confusion/distrust and entrenched partisan politicians are the main reasons voting reform has been so unsuccessful."

I'd rephrase that: "Entrenched partisan politicians IS the main reasons voting reform hasn't happened. "

How about: "Entrenched partisan politicians (elected by confused/distrustful American voters) is the main reason voting reform hasn't happened."

In places were voting reform has happened, for instance, almost everywhere there is a democracy except America, and some places in america, the citizens have been very happy with it and not at all confused.

We know this from surveys and what not.  It's empirical.

There are multiple examples of voting reforms where (nonpartisan) citizens have been unhappy and confused:

http://www.rangevoting.org/Irvtalk.html

[Kevin Baas]

Before I forget - now you know mostly what went through my head in those 5 seconds of simulation after which I concluded it sucks.

A little more: I realized its's a "limit case" that couldn't be compared with transferable vote because it's not possible to transfer, so I considers the case of 2 votes and the behavior as the limit is approached.

Even with 2 votes, transferable votes are still better than non/transferable, and non-transferable is still less gerrymander-resistant than single winner plurality.

Now behavior as it approaches - 2 transferable votes is worse than 4 is worse than 8.... It gets worse monotonically.

So that's about what those 5 seconds consisted of.

Now to read what you wrote...

[Kevin Baas]

Okay first part - when I said "fairly proportional despite" I did not mean to rule our cases of extreme disproportionality.

Second part - when I used an extreme case, I did not mean to imply that all cases were extreme, only to elucidate a pathology.

[Kevin Baas]

First part - mmm... I guess I can't argue with that.

Second part: an exception, even multiple exceptions, do not disprove a rule.

[Brian Langstraat]

"Adding a SNTV simulation to your SI_simulation code should be fairly simple "

Simpler than you think.  Just add a "1" to the number of votes per ballot inputs.

Could you send me any simulation results for SNTV?

If the SNTV has worse results than single-winner plurality elections, then we can confirm your assumption.

Not an assumption.  A deduction.  Part of which I explained to you already.

Do you have simulated results for single-winner plurality elections for multiple districts?

"My suspicion is that the simulations for the non-transferable voting systems are allowing majorities with multiple votes to overwhelm minorities."

Nope.  Quite the opposite: The problem is that a ballot is not removed after it is used to meet a quota.  Thus it gets used twice.  So the people voting for the majority actually get multiple votes, instead of just 1.  Meanwhile the ones that vote for a minority never get their vote used to meet a quota even once.

Not the opposite, since we seem to agree.  With multiple votes, the majority overwhelms the minority, since the majority can meet the quota on multiple candidates while the minority does not meet the quota on any candidates.

The golden rule of counting -- count each element exactly once -- is met by SNTV.

Excessive votes do "get thrown out" in SNTV, which is probably its biggest issue.  Parties, candidates, and supporters would need to plan strategically to maximize their chances of success.

Your example shows how transferable voting systems are better than SNTV, but not how single-winner plurality elections are better than SNTV.

If this multi-member district is split up into 4 single-member districts, there are scenarios where Party 1 wins one district (99 votes) and Party 2 wins three districts (33 each).

[Kevin Baas]

To be clear the golden rule of counting is definitely violated by SNTV. If you carefully apply the logic I explained, you will see that.

I can run it in my free time on SNTV an share the results, but before doing so I must caution:

The results of a simulation are inexorably biased to the scenarios that one simulates.

In matters like this, logic always trumps evidence.

That may sound backwards. But it is how science works. Th evidence is used to INFORM the reasoning. If it contradicts a deduction, that deduction is wrong. Yes. But a deduction that is not contradicted by any evidence, and reasoned soundly from valid premises, is still, at least tentatively, correct.

This is programming. This is algorithms. One does not verify an algorithm by testing a small subset of possible inputs. One verified an algorithm by confirming that the business rules are correct, and that the logic of the algorithm exactly matches the business rules.

In our case, we have 1 business rule: count each ballot exactly once.

That rule is violated.

[Brian Langstraat]

Even with 2 votes, transferable votes are still better than non/transferable, and non-transferable is still less gerrymander-resistant than single winner plurality.

I agreed earlier (Feb 23) that Single Transferable Vote would be better (in most scenarios - http://rangevoting.org/IrvPathologySurvey.html) than SNTV.  Of course, the election results will become more proportional as the number of transferable votes increases.

However, I do not agree that SNTV is less gerrymander-resistant than single-winner plurality voting in multiple districts.  Equivalently, you are saying that a multi-winner district is easier to gerrymander than multiple single-winner districts when both use voting systems with single non-transferable votes. How is this possible?  I thought that the difficulty of gerrymandering increased as the the number of winners increased (and number of districts decreased).

state congress composition tends to be pretty proportional to the state popular vote, despite being elected by single-winner plurality.

 For example, Wyoming went about 65% R and 25% D for president and their single at-large representative, but their combined state congress was about 85% R and 15% D. http://www.nytimes.com/elections/results/wyoming

when I said "fairly proportional despite" I did not mean to rule our cases of extreme disproportionality.

Looking at other results from the nytimes link, states vary in their proportionality.  There are many variables and "noise" in these results, but conclude that:

In general, state congress composition tends to be less proportional as political polarization increases.  This is likely caused by the interaction between gerrymandering and single-winner plurality voting.

A 90%/10% split is rare.

If SNTV was used and a single party was that dominant, then parties would run multiple candidates or third parties/ independents would run.

when I used an extreme case, I did not mean to imply that all cases were extreme, only to elucidate a pathology.

A 90%/10% split is a good counterexample against SNTV.  I think that the main proportionality weaknesses of SNTV are popular candidate receiving too many votes (and hurting similar candidates) and several unpopular, similar candidates receiving a too few votes (and all losing).  However, these weaknesses would be reduced since:

Parties, candidates, and supporters would need to plan strategically to maximize their chances of success.

This was how SNTV worked in countries like Japan. http://archive.fairvote.org/reports/1995/chp7/lundberg.html

an exception, even multiple exceptions, do not disprove a rule.

Your statement is not logical. An empirical rule (proposition) that has an exception (contradiction) is logically false.

Proposition:

In places were voting reform has happened, the citizens have been very happy with it and not at all confused.

We know this from surveys and what not.  It's empirical.

Contradiction:

There are multiple examples of voting reforms where (nonpartisan) citizens have been unhappy and confused:

http://www.rangevoting.org/Irvtalk.html

Thus, the proposition of "In places where voting reform has happened, the citizens have been very happy with it and not at all confused." was logically false.

The proposition of "In most places where voting reform has happened, most of the citizens have been happy with it and not confused." may be logically true.  Could you point to research on the high success of voting reforms?

To be clear the golden rule of counting is definitely violated by SNTV.  If you carefully apply the logic I explained, you will see that.

Definition:

The golden rule of counting = count each element exactly once

Proposition:

The golden rule of counting is definitely violated by SNTV.

Contradiction:

In SNTV, people count each element (vote) exactly once. (In transferable and reweighed voting, people count some elements (votes) multiple times.

Thus, the proposition of "The golden rule of counting is definitely violated by SNTV." is logically false.

Therefore, the conclusion is "The golden rule of counting is met by SNTV." is logically true.

I can run it in my free time on SNTV an share the results, but before doing so I must caution:

I understand that simulations do not perfectly represent reality.  There can be many flaws with simulations.  However, comparing a simulated SNTV to the other voting systems that you have already simulated may give us a good point of comparison.

Proposition:

In matters like this, logic always trumps evidence.

Contradiction:

If it (evidence) contradicts a deduction (logic), that deduction (logic) is wrong.

Thus, the proposition "In matters like this, logic always trumps evidence." is logically false.

Therefore, the proposition "In matters like this, logical deductions must be modified when presented with contradictory evidence."

Hypotheses (logical deductions) are never assumed to be correct or incorrect and only gain credibility as theories after being thoroughly tested with a substantial amount of supporting evidence without contradictory evidence.  This is how science works. https://en.wikipedia.org/wiki/Scientific_method

My proposition (from Feb 23) is:

SNTV may be the simplest change to multi-winner elections (where voters can vote with up to the number of open positions) that would reduce the chances of winner-takes-all by the majority (Approval Voting).  

Do you have any contradictions such as a simpler change?  I hope so, because I am not a fan of SNTV.

[Kevin Baas]

So many things wrong with your reply that I've already explained, it's just not worth the effort.

I don't think you're making an honest effort to understand, so I'm not going to waste my time anymore.

[Kevin Baas]

What really astonishes me is that you respond "if evidene contradicts a deduction, that deduction is wrong." -- which is almost exactly what I said! And then you proceded to paraphrase the entire statement following my initial catch statement.

It's like you feel that you can contradict what I said by saying THE EXACT SAME THING THAT I SAID!

[Brian Langstraat]

Kevin,

I appreciate your time and effort in discussing this topic with me.  In my previous reply, I was trying to make an honest effort to understand your positions and clarify my own positions in a logical way.  If you have any simulation results for SNTV, then I would be very interested in seeing them.

This Topic has over 20 Posts by just 2 Authors which makes contributions from other authors difficult, so I have created a new Topic that can condense and continue this discussion:

Single Non-Transferable Vote (SNTV) (https://groups.google.com/forum/#!topic/electionscience/qM-pTJFLTZA)

Thank you,

Brian