Cumulative voting and minority rights

[J. J.]

On 2/9/2024 at 2:21 PM, Atul Kapur said:

I believe that is an error to take the fact that the rule, among other things, gives the minority the ability to utilize a particular tactic and claim that therefore this is a "rule protecting a minority of a particular size", particularly since there is no guarantee that the tactic will be successful.

 

The tactic, however, will be successful, if the minority passes a certain threshold in the proportion of votes.  That will always be at a point of less than 1/3 at least in this example. 

 

 

 

 

 

[Shmuel Gerber]

On 2/9/2024 at 3:12 PM, Dan Honemann said:

But since the election will be held by cumulative voting regardless of what they wanted, all of the rules relating thereto will be in full force and effect.  

I don't see how it could be otherwise. The election will be held by ballot, so any effect that abstentions and yes votes in voting on the motion to suspend the rules will have on the election will affect all voters equally.  

If I vote no or abstain on a motion to reconsider, do I lose any of my rights on reconsideration if the motion to reconsider is adopted?

I think I am lost at this point, so let's go back to an earlier question. You had asked:

"So what would you say is the vote required to suspend a rule requiring a three-fourths vote for the adoption of a particular motion?"

My answer is a three-fourths vote. I believe this question is discussed in PL with regard to a rule requiring a three-fourths vote* to allow non-members on the floor. My copy of PL is currently further than my elbow (not counting any online edition that I could access with my thumbs), but my recollection is that the General says this rule could only be suspended by a three-fourths vote (so that there would be little reason to adopt such a suspension of the rules).

Now suppose that instead of a motion to suspend the rules and admit a non-member to the floor, a motion (for sake of discussion, let's call it a main motion) to admit a non-member is already pending, and someone moves to suspend the rules in order that the pending motion can be adopted by a two-thirds vote. 

I would say that this motion also requires a three-fourths vote. However, I must be missing something about what you've been saying (about fifty times), because if we need to know in advance how many members will vote on the main motion, then there is not actually any particular size minority protected by the rule? 

Edited February 13, 2024 at 04:54 PM by Shmuel Gerber

[Shmuel Gerber]

*Or maybe it was a four-fifths vote discussed in PL? 

[Dan Honemann]

On 2/13/2024 at 11:53 AM, Shmuel Gerber said:

I think I am lost at this point, so let's go back to an earlier question. You had asked:

"So what would you say is the vote required to suspend a rule requiring a three-fourths vote for the adoption of a particular motion?"

My answer is a three-fourths vote. I believe this question is discussed in PL with regard to a rule requiring a three-fourths vote* to allow non-members on the floor. My copy of PL is currently further than my elbow (not counting any online edition that I could access with my thumbs), but my recollection is that the General says this rule could only be suspended by a three-fourths vote (so that there would be little reason to adopt such a suspension of the rules).

I agree. A minority of a particular size, in this case one-fourth, is protected by the rule.

On 2/13/2024 at 11:53 AM, Shmuel Gerber said:

Now suppose that instead of a motion to suspend the rules and admit a non-member to the floor, a motion (for sake of discussion, let's call it a main motion) to admit a non-member is already pending, and someone moves to suspend the rules in order that the pending motion can be adopted by a two-thirds vote. 

I would say that this motion also requires a three-fourths vote. However, I must be missing something about what you've been saying (about fifty times), because if we need to know in advance how many members will vote on the main motion, then there is not actually any particular size minority protected by the rule? 

I agree.  If a rule is in place requiring a three-fourths vote for the adoption of a motion it will take a three-fourths vote to suspend it because it protects a minority of a particular size (one-fourth).

In neither of these two instances that you mention is there any need to know how many members will vote on the main motion because the fraction used to determine the number of members protected by the rule remains unchanged no matter how many members vote on the main motion.

On the other hand, the fraction used to determine the number of members protected by a rule mandating cumulative voting (as in the case discussed in this thread) will change depending upon the number of members voting in the election. 

 

[Shmuel Gerber]

On 2/13/2024 at 12:51 PM, Dan Honemann said:

On the other hand, the fraction used to determine the number of members protected by a rule mandating cumulative voting (as in the case discussed in this thread) will change depending upon the number of members voting in the election. 

Well, I guess I haven't been able to follow your math on this. I had thought that, aside from variations due to rounding to whole numbers or anomalies arising from a situation in which there is a very small number of voters, the fraction of voters who can elect at least one candidate of their choice by coordinating their cumulative votes remains the same regardless of how many voters there are in total. 

[Dan Honemann]

On 2/13/2024 at 1:27 PM, Shmuel Gerber said:

Well, I guess I haven't been able to follow your math on this. I had thought that, aside from variations due to rounding to whole numbers or anomalies arising from a situation in which there is a very small number of voters, the fraction of voters who can elect at least one candidate of their choice by coordinating their cumulative votes remains the same regardless of how many voters there are in total. 

If you go back and look you will see that I have demonstrated that the fraction will change depending upon the number of voters.  The greater the disparity in number, the greater the change in the fraction.

[Atul Kapur]

On 2/13/2024 at 1:37 PM, Dan Honemann said:

the fraction will change depending upon the number of voters

Which is why I piped up to say the fraction used should be the smallest possible fraction: one member.

Again, this assumes that cumulative voting protects a minority, which I do not believe is the case.

[Shmuel Gerber]

On 2/13/2024 at 1:37 PM, Dan Honemann said:

If you go back and look you will see that I have demonstrated that the fraction will change depending upon the number of voters.  The greater the disparity in number, the greater the change in the fraction.

I was not able to follow that. You gave several numbers depending on "my scenario" (Dan) or "your scenario" J. J., but I don't see where those numbers are coming from. 

[J. J.]

On 2/13/2024 at 1:37 PM, Dan Honemann said:

If you go back and look you will see that I have demonstrated that the fraction will change depending upon the number of voters.  The greater the disparity in number, the greater the change in the fraction.

The fraction itself will not change. The numeric value of what the fraction equals, in this case 7/8, will possibly change, base on the number of votes cast. 

If some thing requires a 2/3 vote, and there are 30 votes, that thing requires 20 or more votes.  If some thing requires a 2/3 vote, and there are 60 votes, that thing requires 40 or more votes.  The fraction is still 2/3 in both cases. 

[Dan Honemann]

On 2/13/2024 at 1:41 PM, Shmuel Gerber said:

I was not able to follow that. You gave several numbers depending on "my scenario" (Dan) or "your scenario" J. J., but I don't see where those numbers are coming from. 

Mr. Martin’s scenario:

There are four members to elect to the committee. 120 members vote, a majority of which is 61. An individual member could cast, at most, four votes for one candidate. 61 divided by 4 is 15.25. Therefore, a minimum of 16 members would need to vote for a candidate in order to ensure his election. The fraction of members protected by the rule, therefore, is 2/15 (13.33%).   

Under my scenario:

There are four members to elect to the committee. 20 members vote, a majority of which is 11. An individual member could cast, at most, four votes for one candidate. 11 divided by 4 is 2.75.  Therefore, a minimum of 3 members would need to vote for a candidate in order to ensure his election. The fraction of members protected by the rule, therefore, is 3/20 (15%)

 

[J. J.]

On 2/13/2024 at 3:12 PM, Dan Honemann said:

Mr. Martin’s scenario:

There are four members to elect to the committee. 120 members vote, a majority of which is 61. An individual member could cast, at most, four votes for one candidate. 61 divided by 4 is 15.25. Therefore, a minimum of 16 members would need to vote for a candidate in order to ensure his election. The fraction of members protected by the rule, therefore, is 2/15 (13.33%).   

Under my scenario:

There are four members to elect to the committee. 20 members vote, a majority of which is 11. An individual member could cast, at most, four votes for one candidate. 11 divided by 4 is 2.75.  Therefore, a minimum of 3 members would need to vote for a candidate in order to ensure his election. The fraction of members protected by the rule, therefore, is 3/20 (15%)

 

Assuming that the quorum was met, no.

First of all, a majority is any number over 10 in this case.  It is 11 in whole numbers, but that not the definition of a majority (44:1).  

Calculating the minority protected is any number greater than half of the votes cast divided by the number positions or slots to be elected.  So the minority is any number greater than 10 / 4 or 2.5.  If more than 2.5 votes are cast against suspending the rule 25. 7 (second line applies). 

The rule protects a minority of greater than 1/8.  There may easily be situations where more than 1/8 will vote against suspension. 

[Shmuel Gerber]

I don't understand any of these complicated calculations or where they're coming from.

In an election of four committee members in which cumulative voting is allowed, a minority of more than 1/5 (that is, more than 1/(4+1), or 20% of the votes cast) is guaranteed election of one candidate of their choice if they put all of their votes on that choice. 

Therefore, it seems to me, suspending the rule permitting cumulative voting where there are four winners to be elected cannot be done by less than a 4/5 vote. 

As far as where a majority enters the calculation, I don't think a majority vote is generally needed for cumulative voting, but Mr Martin has opined here that if it is, what is required is for a candidate to obtain a number of votes that is more than half of the number of ballots cast.

Here, if more than 1/5 of the voters cast each of their four votes for a single candidate, that candidate's votes will exceed 4/5 of the number of ballots cast, which is easily a majority. 

Now if there are some other calculations (which I don't understand) that show that even 20% or less can somehow be sure to elect a candidate depending on how many votes are cast, that certainly should not mean that the rule can be suspended by a 2/3 vote rather than a 4/5 vote! 

If someone can tell me where I've gone wrong, I would appreciate it. Although I would prefer to be told that I am absolutely correct. 🙂

[J. J.]

On 2/13/2024 at 4:12 PM, Shmuel Gerber said:

If someone can tell me where I've gone wrong, I would appreciate it. Although I would prefer to be told that I am absolutely correct. 🙂

I'm not certain if you are wrong, but here is how I would express it.

The minority protected is the minimum number that could, based on the number of members voting, elect one person to that office.

The minimum number that could elect, the minority protected (M), is any number greater than the total number voting (TV), divided by two (2), divided by the number of positions (P).  It would expressed as M > (TV/2) / P.  Any number of votes equal to or greater than M would bean that the rule could not be suspended.

If 120 people vote, M is any number greater than (120/2) / 4 or 60 / 4 or 15.  The minority protected is any number of votes greater than 15.  That is because that, in this circumstance, it will take something more than 15 voters to give their candidate a majority.

If 20 people vote, M is any number greater than (20/2) / 4 or 10/4 or 2.5.  The minority protected is any number of votes greater than 2.5.  That is because that, in this circumstance, it will take something more than 2.5 voters to give their candidate a majority.

I am not certain if that what you are saying. 

 

Edited February 13, 2024 at 09:50 PM by J. J.

[Atul Kapur]

On 2/13/2024 at 4:40 PM, J. J. said:

The minority protected is the minimum number that could, based on the number of members voting, elect one person to that office.

You cannot state that and, at the same time say

On 2/13/2024 at 3:10 PM, J. J. said:

The fraction itself will not change.

because it is dependent on the number of people voting.

[Yes, I recognize you didn't say them at the same time, but in the same thread is still close enough to create the inconsistency].

On 2/13/2024 at 4:12 PM, Shmuel Gerber said:

even 20% or less can somehow be sure to elect a candidate depending on how many votes are cast

Depending on how many votes are cast, one person could be enough to elect a candidate.

We don't know how many will vote in the election. There is no reason to assume it is the same number as vote on the rule suspension (although that is likely the maximum). Hence the safest (ie most protective) assumption is to assume the smallest minority, one member.

[I'm again very glad that this is an imaginary scenario.]

[J. J.]

On 2/13/2024 at 4:12 PM, Shmuel Gerber said:

I don't understand any of these complicated calculations or where they're coming from.

In an election of four committee members in which cumulative voting is allowed, a minority of more than 1/5 (that is, more than 1/(4+1), or 20% of the votes cast) is guaranteed election of one candidate of their choice if they put all of their votes on that choice. 

 

Let me try too understand.

You are opining that is all cases, if 20% of the voters cast all their votes for one candate that this candidate is assured of election.  Is that correct?

If so, the minority protected is 20% because, in all cases, 20%is guaranteed of electing their one candidate.  It that correct?

[Shmuel Gerber]

On 2/13/2024 at 4:56 PM, Atul Kapur said:

Depending on how many votes are cast, one person could be enough to elect a candidate.

Suppose an election rule said directly that a 4/5 vote is required for a candidate to attain the position. Would you still say that something other than a four-fifths vote is needed to suspend the rules, because the election may be decided by one vote? Or that we cannot know what vote is needed because we won't know how many votes will be cast in the election until the actual vote on the election is taken? 

It seems that there are (at least) two separate discussions going on here. Dan Honemann has already agreed that if the fraction of votes necessary remains constant, then the vote to suspend the rules is dependent on that fraction regardless of how many actually vote. The way I see it, the rule in this case (cumulative voting that started the thread) protects a minority of greater than one fifth.

If you want to argue that even if the fraction remains constant, there's no definite minority because the number changes depending on how many vote, that is another discussion. 

[Shmuel Gerber]

On 2/13/2024 at 5:02 PM, J. J. said:

Let me try too understand.

You are opining that is all cases, if 20% of the voters cast all their votes for one candate that this candidate is assured of election.  Is that correct?

If so, the minority protected is 20% because, in all cases, 20%is guaranteed of electing their one candidate.  It that correct?

Not exactly 20%, but any number greater than 20%.

[J. J.]

On 2/13/2024 at 4:56 PM, Atul Kapur said:

You cannot state that and, at the same time say

because it is dependent on the number of people voting.

[Yes, I recognize you didn't say them at the same time, but in the same thread is still close enough to create the inconsistency].

Depending on how many votes are cast, one person could be enough to elect a candidate.

We don't know how many will vote in the election. There is no reason to assume it is the same number as vote on the rule suspension (although that is likely the maximum). Hence the safest (ie most protective) assumption is to assume the smallest minority, one member.

[I'm again very glad that this is an imaginary scenario.]

No, the fraction will always remain the same.  Assume that Mr. Gerber is correct.  The minority protected by the rule would always be 1/5 or 20%.

It is like saying a rule protects a minority of 1/3.  One third of the people voting might be 10 members (30 voting), butit could be 50 members (150 voting). The fraction remains the same.

[J. J.]

On 2/13/2024 at 5:06 PM, Shmuel Gerber said:

Not exactly 20%, but any number greater than 20%.

Okay, I can see that. 

M = Minority Protected

T = Total voters casting at least one vote

P = Number of  Positions

M > T / (P+1)

M > 120/(4+1)

M > 24 

A negative vote of any number greater than 24 will prevent the rules from being suspended.

Is that correct? 

Edited February 14, 2024 at 03:25 PM by J. J.
Clarified T

[Atul Kapur]

On 2/13/2024 at 5:05 PM, Shmuel Gerber said:

Suppose an election rule said directly that a 4/5 vote is required for a candidate to attain the position. Would you still say that something other than a four-fifths vote is needed to suspend the rules

In the situation you describe, it would take a four-fifths vote to suspend. 

That is a fixed fraction. The difference is (or, perhaps, was) that under J.J.'s formula, the fraction changed depending on the number of votes: 

M > (TV/2) / P

On 2/13/2024 at 5:05 PM, Shmuel Gerber said:

Dan Honemann has already agreed that if the fraction of votes necessary remains constant, then the vote to suspend the rules is dependent on that fraction regardless of how many actually vote.

Of course I agree with that. I'm not trying to create a new rule.

I have emphasized the 'if' in that quote because J.J.'s formula did not meet the condition that followed.

On 2/13/2024 at 5:07 PM, J. J. said:

Assume that Mr. Gerber is correct.  The minority protected by the rule would always be 1/5 or 20%.

J.J., have you changed your position and moved away from the formula you had previously used? I see that you've edited your post to strike that out.

If you now agree with Mr. Gerber, then that changes things and makes them somewhat simpler. If you would also agree that cumulative voting does not protect a minority,that would simplify things immensely. 

Added:

Our posts coincided and I see that you are still using a formula that incorporates the total votes cast

M > T / (P+1)

So it is still not possible to say that the fraction is constant, therefore requiring its conversion to a number. In this situation, I maintain that the number is one.

@Shmuel Gerber, I suggest that if there are two discussions going on here, that this is where they divide: whether the fraction is constant.

Edited February 13, 2024 at 10:36 PM by Atul Kapur

[J. J.]

On 2/13/2024 at 5:26 PM, Atul Kapur said:

J.J., have you changed your position and moved away from the formula you had previously used? I see that you've edited your post to strike that out.

If you now agree with Mr. Gerber, then that changes things and makes them somewhat simpler. If you would also agree that cumulative voting does not protect a minority,that would simplify things immensely. 

First of all, as I've said, I'm not wedded to any specific proposition.

However, Mr. Gerber's case makes a strong argument that this does protect a minority, a minority  large enough to always elect.  The fraction is always there and is unchanged by the number of people voting.  It changes only the numerator, but not the fraction. 

 

[Shmuel Gerber]

On 2/13/2024 at 5:26 PM, Atul Kapur said:

Our posts coincided and I see that you are still using a formula that incorporates the total votes cast

M > T / (P+1)

So it is still not possible to say that the fraction is constant, therefore requiring its conversion to a number. In this situation, I maintain that the number is one.

@Shmuel Gerber, I suggest that if there are two discussions going on here, that this is where they divide: whether the fraction is constant.

I don't understand this at all. When we say "four-fifths vote," we are talking about four-fifths of the votes cast. That is the fraction which remains constant regardless of the number of votes cast. 

Edited February 13, 2024 at 10:42 PM by Shmuel Gerber

[Shmuel Gerber]

On 2/13/2024 at 5:21 PM, J. J. said:

M = Minority Protected

T = Total votes

P = Number of  Positions

M > T / (P+1)

M > 120/(4+1)

M > 24 

A negative vote of any number greater than 24 will prevent the rules from being suspended.

Is that correct? 

I would say yes, but apparently there's still some confusion (and I do not understand why) about what "total votes" means and how it affects the formula. 

[J. J.]

On 2/13/2024 at 5:45 PM, Shmuel Gerber said:

I would say yes, but apparently there's still some confusion (and I do not understand why) about what "total votes" means and how it affects the formula. 

Total votes are total number of votes cast, excluding abstentions (obviously by legitimate voters at a properly called meeting). 

Edited February 13, 2024 at 10:52 PM by J. J.

[Dan Honemann]

On 2/13/2024 at 4:12 PM, Shmuel Gerber said:

In an election of four committee members in which cumulative voting is allowed, a minority of more than 1/5 (that is, more than 1/(4+1), or 20% of the votes cast) is guaranteed election of one candidate of their choice if they put all of their votes on that choice. 

I believe these two things to be true:

1. If 120 members vote in an election to elect 4 members to a committee, a candidate must receive at least 61 votes in order to be elected.

2. The minimum number of members that can cast at least 61 votes for a candidate is 16.  This, then, is the number of members protected by the rule. 

Do you (Mr. Gerber, that is) disagree with either or both of these statements?