Cumulative voting and minority rights

[J. J.]

On 2/15/2024 at 11:40 AM, Dan Honemann said:

While you are waiting for a response from Dr. Kapur, I can't help but feel it a bit strange to refer to "any number greater than 1/5" as being the number of members protected by a rule. I suppose lots of numbers will be greater than 1/5. Do you mean the smallest one of these numbers?

Would you say any number greater than one half as being a majority is a bit strange?   I don't.

 

[Atul Kapur]

J.J.'s latest question was

Quote

I would be interested in hearing Dr. Kapur's premise that the rule does not protect a minority of, in this case, less than 1/3.

For me, the crux of the issue is not the size of the minority but, rather, whether the rule protects a minority.

J.J.'s original question was

On 2/5/2024 at 12:20 PM, J. J. said:

1.  Does cumulative voting protect a "minority of a particular size," within the meaning of 25:2 #7?  (I will go with yes, currently.)

Mr. Honemann responded, way back on page 1 of this thread,

On 2/7/2024 at 2:13 PM, Dan Honemann said:

I do not think that the rule in 46:43 protects "a minority of a particular size" as contemplated by the rule in 25:2(7).

(I am not certain that he continues to hold this view, although he did repeat it as late as page 3.)

I am of the opinion that cumulative voting does not "protect a minority" and definitely does not, as J.J. said, 

On 2/7/2024 at 1:55 PM, J. J. said:

creates a right for a "minority group."

46:43 provides no right to the minority group to elect a candidate. It only provides the possibility to use a tactic. "A minority group, by coordinating its effort in voting for only one candidate who is a member of the group, may be able to secure the election of that candidate as a minority member of the board." (emphasis added)

It is not correct to label this possibility as a right.

[J. J.]

On 2/15/2024 at 2:03 PM, Atul Kapur said:

46:43 provides no right to the minority group to elect a candidate. It only provides the possibility to use a tactic. "A minority group, by coordinating its effort in voting for only one candidate who is a member of the group, may be able to secure the election of that candidate as a minority member of the board." (emphasis added)

It is not correct to label this possibility as a right.

It does give a minority of less than one third (where there are more than 2 positions to be elected), the ability to elect one person in all cases.  That seems to be more than a possibility. 

If there were a rule that said "a vote of one fourth shall require a roll call," that rule only gives 1/5 the possibility of ordering a ballot; maybe when the stating vote is taken, less than 1/4 vote in favor of a roll call.  Yet, even with this possibility, is there any question that the rule protects a minority of any percentage greater than or equal to 1/4 and that this rule could not be suspended by a vote of less than 3/4 of the voters? 

[Dan Honemann]

On 2/15/2024 at 1:40 PM, J. J. said:

Would you say any number greater than one half as being a majority is a bit strange?   I don't.

 

Yes, any number greater than one-half will be "more than half", which is the definition of a  "majority" for purposes of determining the outcome of a vote.

However, I think that only one number or fraction can constitute "a particular size", such as "one-fourth" or "one-fifth" for purposes of 25:2(7).  It is true, of course, that if a rule protects a minority of one-fourth or one-fifth, any fraction less than that will also be protected, but there has to be that fraction of a particular size to begin with.

[J. J.]

On 2/15/2024 at 2:56 PM, Dan Honemann said:

Yes, any number greater than one-half will be "more than half", which is the definition of a  "majority" for purposes of determining the outcome of a vote.

However, I think that only one number or fraction can constitute "a particular size", such as "one-fourth" or "one-fifth" for purposes of 25:2(7).  It is true, of course, that if a rule protects a minority of one-fourth or one-fifth, any fraction less than that will also be protected, but there has to be that fraction of a particular size to begin with.

Mathematically, it can be properly expressed as a "particular size." 

It seems clear that "the minority protected by the rule," in this case is any minority larger that 1/5.  It is similar to saying, correctly, that a majority is any number greater than one half, whether that is a number greater than 51/101, or 101/200, or 501/1000.  Majority still equals any number greater than 1/2 of the votes cast, much like a minority would constitute any number less than or equal to one half of the votes cast.

"Particular" means "of, relating to, or being a single person or thing."  That looks it would be the particular size of the the minority, in the given situation. 

[Atul Kapur]

On 2/15/2024 at 2:03 PM, Atul Kapur said:

For me, the crux of the issue is not the size of the minority but, rather, whether the rule protects a minority.

 

On 2/15/2024 at 2:34 PM, J. J. said:

It does give a minority of less than one third (where there are more than 2 positions to be elected), the ability to elect one person in all cases.  That seems to be more than a possibility. 

I think I see where the difference in interpretation is coming from. The protection referred to in 25:2(7) is to a minority, which only comes into  existence when a vote is taken and is less than a majority; it is not pre-defined. The benefit of cumulative voting is to a minority group, which is pre-defined and needs to plan to coordinate its actions before the vote is taken. 

Therefore, the protection in 25:2(7) does not apply to the question posed in the OP.

Edited February 16, 2024 at 10:46 PM by Atul Kapur
corrected typo in ronr reference

[J. J.]

On 2/15/2024 at 5:37 PM, Atul Kapur said:

 

I think I see where the difference in interpretation is coming from. The protection referred to in 25:2(7) is to a minority, which only comes into  existence when a vote is taken and is less than a majority; it is not pre-defined. The benefit of cumulative voting is to a minority group, which is pre-defined and needs to plan to coordinate its actions before the vote is taken. 

Therefore, the protection in 26:25:2(7) does not apply to the question posed in the OP.

A minority (of more than one) will always be a group.  It would not necessarily pre-plan action, as in the case of the castor of vote 25. 

[Atul Kapur]

But pre-planning is necessary for the particular result that you are claiming is protected. To use an earlier example, "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?" 

Suspending this rule requires a 3/4 vote because it protects a minority of more than 1/4 - any minority of that size, no matter who makes up that minority (ie, no coordination of votes required), and whether or not that minority exists is only known when the result of the vote is announced.

On the other hand, the minority group, which is able to use a tactic under cumulative voting, is pre-defined and needs to coordinate its votes to be certain of electing a preferred candidate. This is not the same thing and this minority group is not what is envisaged by 26:2(7). What if not all members of the group follow the plan when casting their cumulative votes? The "guarantee" (or protection) is shown to be a mirage.

Protecting a minority of a particular size is not the same as protecting a minority group (aka faction) if it happens to be of a particular size.

Edited February 15, 2024 at 11:22 PM by Atul Kapur

[J. J.]

No, pre-planning is not necessarily, as was demonstrated.  The minority may be an ad hoc one.  Further, no group could enforce how to vote on even a minority. 

[Shmuel Gerber]

On 2/5/2024 at 12:20 PM, J. J. said:

The society adopts the special rule that says:  "The ABC Committee shall consist of four members of the assembly, elected by cumulative voting," 

 

On 2/15/2024 at 2:56 PM, Dan Honemann said:

I think that only one number or fraction can constitute "a particular size", such as "one-fourth" or "one-fifth" for purposes of 25:2(7).  It is true, of course, that if a rule protects a minority of one-fourth or one-fifth, any fraction less than that will also be protected, but there has to be that fraction of a particular size to begin with.

In the example initially given in this thread, the rule protects a minority of greater than one fifth. If the number of members on the committee were different, then this fraction would be different. But since this committee is of a particular size, and is even stated that way in the rule, then the minority protected is also of a particular size.

(I'm not conceding that if the number of seats varied then there would not be any minority of a particular size protected in each case where the rule is applied; but where the number of seats is fixed, as here, then I think there certainly is a minority of a particular size protected by the rule.)

If there is a problem with the "greater than" part of this formulation, then the same problem would exist with a rule requiring a four-fifths vote for adoption of a motion, which protects not a minority of one fifth, but a minority of greater than one fifth. This is much in the same way that the requirement of a 2/3 vote to close debate on a motion protects a minority of greater than 1/3 but not of 1/3.

[Dan Honemann]

On 2/15/2024 at 8:56 PM, Shmuel Gerber said:

If there is a problem with the "greater than" part of this formulation, then the same problem would exist with a rule requiring a four-fifths vote for adoption of a motion, which protects not a minority of one fifth, but a minority of greater than one fifth. This is much in the same way that the requirement of a 2/3 vote to close debate on a motion protects a minority of greater than 1/3 but not of 1/3.

Thanks.  I think I may finally be coming to grips with the numbers involved.  I gather now (it's about time, one might say) that whenever 4 positions are to be filled, you are saying that the rule protects a minority of the same size as if a 4/5 vote were required for election, since a vote of this size will guarantee election. This fraction of members protected by the rule will vary depending upon the number of seats to be filled, but can be determined by use of the same formula.*  

The question remains as to whether this is the sort of "minority of a particular size" contemplated by 25:2(7).  Agreeing with Dr. Kapur, I remain of the opinion that it is not.  I am also still of the opinion that the rule is a suspendible rule, a two-thirds vote being required for adoption.

---------------------------------

* If I still have this wrong, just say so and don't waste your time bothering to tell me why. 

 

[Shmuel Gerber]

On 2/16/2024 at 7:36 AM, Dan Honemann said:

Thanks.  I think I may finally be coming to grips with the numbers involved.  I gather now (it's about time, one might say) that whenever 4 positions are to be filled, you are saying that the rule protects a minority of the same size as if a 4/5 vote were required for election, since a vote of this size will guarantee election. This fraction of members protected by the rule will vary depending upon the number of seats to be filled, but can be determined by use of the same formula.*  

---------------------------------

* If I still have this wrong, just say so and don't waste your time bothering to tell me why. 

Almost. If I understand the math correctly myself:

I don't think a 4/5 vote will guarantee election of all four seats of the majority's choice, but a vote of greater than 1/5 will guarantee election of one seat of the minority's choice. If the factions were split exactly 4/5 to 1/5, then the best the majority could do to prevent election of the minority's choice (and vice versa) is to create a tied vote so that no one is elected.

I think the math will be easier with 100 voters instead of 120, so suppose there are 100 voters. A faction of 20 members cast all their votes for candidate A: 20*4=80.

Now, in order to defeat candidate A, the rest of the voters must all (collectively) cast at least 80 votes for each of four other candidates. But in order to have enough votes for that, they also cannot cast more than 80 for any one, because then there would be less than 80 for another. So either the vote would be tied all around, or candidate A gets a seat.

Edited February 16, 2024 at 01:53 PM by Shmuel Gerber
inserted the underlined word

[J. J.]

The problem with Dr. Kapur's premise is that it assumes coordination of the minority and it implies that this minority is needed to elect.

Even in the example, one person is shown not coordinating his votes and voting for four candidates.  Several others could do the same.

In this example, there are five candidates, G, H, J, K, & M.  120 voters each cast 4 votes for the seats, using cumulative voting.  Voting is done by a non secret ballot.

Ballots 1-20 has all 4 votes for G (80 votes)

Ballot 21-24 has three votes for G (12 votes), and one vote for J (4)

Ballot 25  1 vote each for G,  H, J, & K.

Ballot 26-100 has one vote each for H, J, K, & M (each get 75 votes)

Ballot 101-120 H gets all four (80 votes)

The total are:

G gets 93 votes

H gets 156 votes

J gets 80 votes

K gets 76 votes

M gets 75 votes

Any number greater than 1/(P+1) absolutely assures an election, but someone could get equal to or less than that amount and still be elected. 

 

[Shmuel Gerber]

On 2/15/2024 at 6:21 PM, Atul Kapur said:

But pre-planning is necessary for the particular result that you are claiming is protected. To use an earlier example, "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?" 

Suspending this rule requires a 3/4 vote because it protects a minority of more than 1/4 - any minority of that size, no matter who makes up that minority (ie, no coordination of votes required), and whether or not that minority exists is only known when the result of the vote is announced.

On the other hand, the minority group, which is able to use a tactic under cumulative voting, is pre-defined and needs to coordinate its votes to be certain of electing a preferred candidate. This is not the same thing and this minority group is not what is envisaged by 26:2(7). What if not all members of the group follow the plan when casting their cumulative votes? The "guarantee" (or protection) is shown to be a mirage.

Protecting a minority of a particular size is not the same as protecting a minority group (aka faction) if it happens to be of a particular size.

This argument seems a bit hair-splitting to me, and I don't find it persuasive. The rule protects a minority of a particular size voting in a particular way. If a minority of that size votes in that way, they get what they want because of this rule, regardless of how anyone else votes. If you take away the rule, then the majority can override their ability to do so, even if they were to coordinate to ensure their desired outcome — which obviously they have the right to do when protected by the rule.

[Dan Honemann]

On 2/16/2024 at 8:49 AM, Shmuel Gerber said:

I don't think a 4/5 vote will guarantee election of all four seats of the majority's choice, but a vote of greater than 1/5 will guarantee election of one seat of the minority's choice.

When I said "will guarantee election" I meant election of the minority's candidate to a seat on the committee. Have I still got this wrong? 

[J. J.]

On 2/16/2024 at 9:29 AM, Dan Honemann said:

When I said "will guarantee election" I meant election of the minority's candidate to a seat on the committee. Have I still got this wrong? 

It has to be greater than 1/5 in this case.  1/5 will not guarantee an election. 

[Dan Honemann]

On 2/16/2024 at 9:39 AM, J. J. said:

It has to be greater than 1/5 in this case.  1/5 will not guarantee an election. 

I didn't say a 1/5 vote would guarantee election, I said a minority of the same size as if a 4/5 vote were required for election.

But I've long ago grown weary of this discussion, so let me cut to the chase. I do not think that a rule mandating cumulative voting is a rule protecting a "minority of a particular size" within the meaning of 25:2(7).  The fact that the fraction of members claimed to be protected by the rule will vary depending upon the number of positions to be filled is in my opinion alone sufficient to indicate that this is true.  I also think there is some merit to the argument put forth by Dr. Kapur, but this is simply an additional reason in support of my opinion. Icing on the cake, so to speak.

I freely admit to being rather obtuse regarding the mathematics you and Mr. Gerber were patiently attempting to explain to me, and for this I apologize.

[Shmuel Gerber]

On 2/16/2024 at 9:29 AM, Dan Honemann said:

When I said "will guarantee election" I meant election of the minority's candidate to a seat on the committee. Have I still got this wrong? 

No, you've got it right.

You said, "whenever 4 positions are to be filled, you [SG] are saying that the rule protects a minority of the same size as if a 4/5 vote were required for election, since a vote of this size will guarantee election." I had read "a vote of this size" to mean a 4/5 vote, but I see now that's not what you meant.

I have indeed been saying that the vote of a minority of the same size protected by a rule requiring a 4/5 vote for election (i.e., more than 1/5) is protected by J.J.'s rule that "The ABC Committee shall consist of four members of the assembly, elected by cumulative voting," since a vote of this size (or rather, this particular size 🙂) will guarantee election of one candidate supported by this minority.

But now that you've made me think about it some more, that is actually understating the case a bit. A rule requiring a 4/5 vote for election provides no protection at all to a minority of exactly 1/5, whereas cumulative voting in an election of 4 seats gives a minority of 1/5 the ability to guarantee either election of the minority's candidate or a stalemate (no election).

Edited February 16, 2024 at 03:26 PM by Shmuel Gerber

[Gary Novosielski]

If I understand Dan's position, he's drawing a distinction between a minority of a particular size, and one of variable size depending upon the number of positions open, the inclination of the minority to work as a team, the barometric pressure and the phase of the moon.

I concur.

If I were in the chair I would probably simply require a two-thirds vote to suspend the rules, and note that, if appealed from, the matter would be decided by a majority vote, which protects no minority at all.

[Shmuel Gerber]

On 2/16/2024 at 1:43 PM, Gary Novosielski said:

If I understand Dan's position, he's drawing a distinction between a minority of a particular size, and one of variable size depending upon the number of positions open, the inclination of the minority to work as a team, the barometric pressure and the phase of the moon.

I concur.

If you have to make the argument sillier to  make the case, then it's a weak argument.

However, to take up one of these points, if a rule provides that adoption of a particular type of motion requires a three-fourths vote during a waxing moon, a two-thirds vote during a waning moon, and unanimous consent during a full moon, I do not see any reason to conclude that this vote requirement may be suspended at any time by a two-thirds vote because no "minority of a particular size" is protected by the rule. On the contrary, the size of the minority protected by the rule is very particular.

And by the way, for quite a while the rule in the U.S. House of Representatives was: "A rule may not be suspended except by a vote of two-thirds of the Members voting, a quorum being present. The Speaker may not entertain a motion that the House suspend the rules except on Mondays, Tuesdays, and Wednesdays and during the last six days of a session of Congress."

[Dan Honemann]

On 2/19/2024 at 12:43 PM, Shmuel Gerber said:

However, to take up one of these points, if a rule provides that adoption of a particular type of motion requires a three-fourths vote during a waxing moon, a two-thirds vote during a waning moon, and unanimous consent during a full moon, I do not see any reason to conclude that this vote requirement may be suspended at any time by a two-thirds vote because no "minority of a particular size" is protected by the rule. On the contrary, the size of the minority protected by the rule is very particular.

So we differ on what does or does not constitute a "particular size" within the meaning of 25:2(7).  Life goes on.

[Shmuel Gerber]

On 2/19/2024 at 1:04 PM, Dan Honemann said:

Life goes on.

At least until Saturday. Then there's a full moon and I can howl again. 🙂

[Atul Kapur]

The administrators of this forum request that new howls be started as a new thread, rather than adding to this already multi-page thread that is figuratively pleading to be closed.