I will actually give a very simple example of why the distribution of voters per party does matter and how no deterministic method can be guaranteed to pass Ossipoff's measure of unbias with no prior knowledge of the distribution.
Imagine you have a region with a stable and polarised electorate and 3/4 of the population always vote A, and 1/4 always vote B. And there are 5 seats on offer. You could give 3 seats to A and 2 to B, or 4 to A and 1 to B. A deterministic method will always give the same result, so whichever result the method picks, there will be a large or small party bias. A non-deterministic method could get round this though. Obviously Ossipoff could claim that this is a contrived distribution. Sure, but so is any distribution and you can't know a priori what distributions will be like in general. This is what I mean when I say that the "bias free" method relies on idealised conditions - conditions that aren't guaranteed in the real world.
One last point - when I talk about Sainte-Laguë being the best measure of proportionality, I have previously quoted Balinski and Peyton Young on this where they say:"Webster's is the unique unbiased divisor method. It seems amazing therefore that Hill's method could have been chosen in 1941 on precisely the ground that it was the unbiased method, and that Webster's method was discarded."which Ossipoff has ignored. When he didn't think I had properly considered a paper by Huntington (that he didn't cite or quote, just gave me vague Google directions), he blocked me. This is major hypocrisy from Ossipoff, but is not surprising. 
Toby

On Friday 19 July 2024 at 10:26:28 BST, Toby Pereira <tdp201b@yahoo.co.uk> wrote:  

I will reply in one block rather than line-by-line, as it might become a bit of a mess.
If you are defining a specific sort of bias, you need to reiterate it in every post you use the term, or at least in every discussion thread. "Bias" is already a word in the English language and you do not have a monopoly over it. The form of bias I was talking about was systemic departure from proportionality in favour of small parties, not non-systemic as you dishonestly or ignorantly claim. I have been quite clear about this. I have also explained at length why Sainte-Laguë is the single most reasonable measure of proportionality and not just any old allocation rule.
What I was referring to in your post about originally accepting that assumptions were required was when you put "If it is equally likely to find a party with its final quotient anywhere in interval N". Note the "if". This seemed to be the assumption that your unbiased method was dependent on. Is it not then?
I've never doubted that your method has interesting theoretical properties under idealised conditions, but when you put things like "Bias-Free is entirely unbiased, without conditions", you're claiming too much and it's simply wrong.
You could even demonstrate to people on this list how your method is unbiased, or provide a link to where you have done so, perhaps with some illuminating examples. Or maybe it's better to insult people. I don't know. It's a close call.

You have a habit of falling out with people on this mailing list. When someone disagrees with you about something, it might be better to try and read and understand where they are coming from, rather than arrogantly assuming from the outset that they can't possibly have a point. Some of my points you have just replied to with insults, suggesting you have no rebuttal to them. Your lack of self-awareness is mind-boggling. The problem is not everybody else.
Toby

On Friday 19 July 2024 at 06:11:52 BST, Michael Ossipoff <email9648742@gmail.com> wrote:  

On Wed, Jul 17, 2024 at 05:50 Toby Pereira tdp201b@yahoo.co.uk wrote:

Nice try, but I'm not the one making such sweeping claims about the method so do not need to define the conditions under which any claims about it hold.

I defined bias, & told how BF is completely unbiased twice at EM. Once when I introduced it in (I believe) 2006, & again in September’23.
No, you don’t have to define what conditions you’re talking about. But when someone can’t say what it is that they mean, it’s probably because they don’t know.

In any case, your "bias free" method certainly is not entirely unbiased without conditions as you claim. For one thing, by the measure that most people would reasonably see as the best measure of proportionality (the Sainte-Laguë measure), "bias free" favours small parties, so that in itself is a form of bias.

As I’ve surely mentioned, Toby hasn’t a clue what bias is. He’s continuing to confuse it with non-systematic departure from proportionality.

But even by that measure, it can quite clearly be shown that any deterministic method (that doesn't award fractional seats, and perhaps other obvious background caveats), can end up biased, depending on how votes are distributed in terms of small/large parties.

There, Toby is confusing the proportionality of a particular allocation with the bias of an allocation-rule.

It's pretty obvious in fact. And back in 2012, you seemed to acknowledge that assumptions were required, but it appears you've forgotten that now. http://lists.electorama.com/pipermail/election-methods-electorama.com//2012-July/095996.html

I’m not entirely sure what Toby is referring to. Warren Smith was making claims about what he felt was needed for defining, measuring & minimizing bias. I’ve never heard of anyone agreeing with him on that.
But, at first, I was willing to discuss how his requirements could be met.
But at least 1 or 2 academic journal papers reported about BF, & one named it the Ossipoff-Agnew method.
Agreement was expressed regarding its unbias.

It is not clear in any case that a method that balances small parties and large parties in this manner is better than one that gives a more mathematically proportional result. E.g. if you have two small parties and two large parties, and the two large parties end up slightly overrepresented and the two small parties underrepresented, this is not necessarily any worse than having one of each over/underrepresented.

Again, completely clueless about what bias is, & the difference between bias & non-systematic disproportionately.
Bias is worse, precisely because it consistently, systematically disfavors certain groups(large or small parties or states).
These things have all been explained to Toby several times, but he’s still reopening exactly the same blather as always.
Assertive, self-assured, & clueless.
In other words, the perfect poster-child for the Dunning-Kruger effect.

You just have four separate parties, two of which end up overrepresented and two under. There's no coalition between parties of similar size so this balancing is not required.

…demonstrating tha whenever it seems that Toby has surely maxed-out, he outdoes himself again.

Perhaps if you continue with your incorrect claims, I will have to block you!

Yes, if that will shut you up.

Toby

On Tuesday 16 July 2024 at 15:26:37 BST, Michael Ossipoff <email9648742@gmail.com> wrote:  

Oops!!! Toby forgot to say what conditions he was referring to. 
Bias-Free is entirely unbiased, without conditions.
I propose Saint-Lague (SL), because of its natural intuitive obviousness, & it’s near-unbias.
Bias-Free (BF) is a refinement that I’d offer as a possibility for later.
On Tue, Jul 16, 2024 at 06:04 Toby Pereira tdp201b@yahoo.co.uk wrote:

It is worth noting that the method Ossipoff declares to be "bias free" is only so under a very specific set of assumptions.
Toby
On Monday 15 July 2024 at 04:38:35 BST, Michael Ossipoff email9648742@gmail.com wrote:

There was interest in a poll about PR. But I feel that first the PR methods should be tried, used,  in a poll with the actual candidates & parties.
As I mentioned before, there’s no substitute for the experience of actually using the electoral methods in polls. You don’t know the methods until you use them.
So I propose a 3-part poll.  …presidential & PR:

1.  A Condorcet presidential-poll with 7 candidates + the approval-line. As others have mentioned, of course it could be counted by any rank-count that allows equal-ranking. But of course RP(wv) won here as the most collectively popular, & so its winner should be reported.
The approval-line of course would allow counting by methods that use explicit-approval.
…in addition to by the zero-cost implementation method.
2. A 3-seat STV poll among the same set of candidates as in the presidential-poll.
…as if we were electing a 3-person presidential triumvirate, or seats in some 3-member district in which those candidates are running.
Of course the STV rankings could be counted by any STV version, & integer STV is (in some ways) an easier count. But fractional STV is the unarbitrary STV that doesn’t require a rule or randomizing-process for the order in which ballots transfer.
Of course, because the STV doesn’t allow equal-rankin, then its ballots also could & would also be counted for an RCV count.
Of course if someone wanted to vote different rankings for STV & RCV, then they could write both & indicate which is which.
3. A 500-seat at-large party-PR allocation election. Of course voters vote for their favorite party, & seats are allocate to the parties in proportion to their votes.
Reported will be: allocations by:
Sainte-Lague, Bias-Free (Ossipoff-Agnew), d’Hondt, Largest-Remainder, & Huntington-Hill (“Equal-Proportions”).
SL & BF probably won’t differ from eachother.
————-
For the party-PR SL & BF allocation of 500 seats, the requirement for a party being seated 🪑 is about 1/7 of one percent of the vote.
For the 3-seat STV allocation, the requirement is being over 1/4 of the vote.
————-
SL, in actual implementations, requires .7 quotas for a party’s 1st seat. That’s to thwart, prevent & discourage splitting-strategy, which could otherwise sometimes be advantageous if the conditions were detected.
Because BF & SL give often the same allocation, then BF should have that same requirement.
That’s taken into account for the abovestated requirement for a party to be seated.
—————- 
Candidates for presidential & STV elections:
(These listings are alphabetical.)
Joe BidenRFK Jr.Chase OliverJill SteinDonald TrumpCornell WestMarianne Williamson approval-line——————————————Parties for party-PR election:
American Independent American Solidarity Constitution DemocratGreenLibertarian Peace & FreedomWorking Family —————Of course if this poll is going to happen, then additional nominations should be allowed. But we probably don’t need a week or two for that.Surely any additional nominations would be made within 2 days. So let’s say that the period for optional additional nominations ends exactly 48 hours after this message posts.
…& that the voting period begins at that same moment.
We don’t need a month for the voting-period, do we? Shall we say 1 week if there’s no electioneering, & 2 weeks if there’s electioneering?
Anyone can change any of their ballots during the voting period.————Of course if this poll happens, & if no one else volunteers to take the responsibility of recording the ballots, then I’ll do so.  …then of course will unblock the people I’ve blocked, for that purpose.————-It goes without saying that anything about the details of this poll could be objected-to, & then, if others support the objection, then discussion would be called-for. 
It’s always best to avoid the delay caused by a procedural vote, & so hopefully there will be a consensus agreement. …or at least it will be informally-obvious which position is supported or acceptable to the most people, based on opinions expressed.
An RP(wv) vote would be a reluctant last-resort. Anyone could call for it if consensus were adamantly refused & no position seemed to clearly have more support or acceptance.
Hopefully none of that will be necessary, but it’s good to have it mentioned for contingency.————-As the proposer of the poll, I should vote first, immediately at the beginning of the voting-period. I don’t know if anyone will participate, but, because there was participation in the previous poll, & because people have suggested a PR poll, & because there’s no substitute for using the electoral methods…then I’ll proceed on the assumption that there’s interest & that there might be participation.
If the poll doesn’t happen, it won’t be because I didn’t try to start it.

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

You missed the point I was making that this isn't a single allocation, but that due to whatever reason, this is a stable population, so there is bias every election. And because we can't know a priori what distributions will be like in general, you might find that "bias free" does in fact favour small or large parties in the long term.
OK, what you actually said was "For one thing I doubt that they said that. It was known, at their time of writing, that SL has some (but very little) bias.
Maybe they said that SL is the only divisor-method ever having been used that is nearly unbiased. …or at least that it was the least biased of all divisor-methods that have been used."
I had put the relevant bit in quotes, because it was a quote not something for you to simply "doubt". When I later pressed this, nothing more was heard from you. Anyway, they said it was unbiased, not the least unbiased of those that currently exist, and you're now trying to claim that it was true at the time because it was the least unbiased. The mental gymnastics you're willing to go through.
Toby
On Saturday 20 July 2024 at 00:24:14 BST, Michael Ossipoff email9648742@gmail.com wrote:

On Fri, Jul 19, 2024 at 15:11 Toby Pereira tdp201b@yahoo.co.uk wrote:

I will actually give a very simple example of why the distribution of voters per party does matter and how no deterministic method can be guaranteed to pass Ossipoff's measure of unbias with no prior knowledge of the distribution.
Imagine you have a region with a stable and polarised electorate and 3/4 of the population always vote A, and 1/4 always vote B. And there are 5 seats on offer. You could give 3 seats to A and 2 to B, or 4 to A and 1 to B. A deterministic method will always give the same result, so whichever result the method picks, there will be a large or small party bias. A non-deterministic method could get round this though. Obviously Ossipoff could claim that this is a contrived distribution. Sure, but so is any distribution and you can't know a priori what distributions will be like in general. This is what I mean when I say that the "bias free" method relies on idealised conditions - conditions that aren't guaranteed in the real world.

Should we laugh or cry?
In Toby’s example, SL, BF, DH & EP (HH) all give the following seat-allocation:
A: 4B: 1
What’s this?!  B should get 1/4 of the seats, but it only gets 1/5!
Bias!!!
Actually, no. As I said, Toby hasn’t a clue what bias is.
As I carefully explained to Toby in the message that he’s “replying to”, bias is systematic, consistent disfavor, in s/v.
Therefore, bias is NOT disproportion in a particular allocation.
The abovestated allocation has DISPROPORTION. 
But, by definition, only an allocation-rule, & NOT a particular allocation, can have bias.
Toby keeps repeating his blather, completely obliviously to what has been explained to him.
Dunning-Kruger is vindicated & demonstrated again!

One last point - when I talk about Sainte-Laguë being the best measure of proportionality, I have previously quoted Balinski and Peyton Young on this where they say:
"Webster's is the unique unbiased divisor method. It seems amazing therefore that Hill's method could have been chosen in 1941 on precisely the ground that it was the unbiased method, and that Webster's method was discarded."which Ossipoff has ignored.

I didn’t ignore it. I merely pointed out that you’re misinterpreting what he meant.
At the time when he said that, BF didn’t exist as an allocation-rule proposal. So, what he said was true at the time when he said it.
Arguably it could be said now too, if the statement is understood to encompass only those allocation-rules that have been used for PR or apportionment.
Among the divisor-methods that have ever been used, SL is the most unbiased & the only one remotely unbiased.
HH/EP is about twice as biased as SL.

On Friday 19 July 2024 at 10:26:28 BST, Toby Pereira <tdp201b@yahoo.co.uk> wrote:  

I will reply in one block rather than line-by-line, as it might become a bit of a mess.
If you are defining a specific sort of bias, you need to reiterate it in every post you use the term, or at least in every discussion thread. "Bias" is already a word in the English language and you do not have a monopoly over it. The form of bias I was talking about was systemic departure from proportionality in favour of small parties, not non-systemic as you dishonestly or ignorantly claim. I have been quite clear about this. I have also explained at length why Sainte-Laguë is the single most reasonable measure of proportionality and not just any old allocation rule.
What I was referring to in your post about originally accepting that assumptions were required was when you put "If it is equally likely to find a party with its final quotient anywhere in interval N". Note the "if". This seemed to be the assumption that your unbiased method was dependent on. Is it not then?
I've never doubted that your method has interesting theoretical properties under idealised conditions, but when you put things like "Bias-Free is entirely unbiased, without conditions", you're claiming too much and it's simply wrong.
You could even demonstrate to people on this list how your method is unbiased, or provide a link to where you have done so, perhaps with some illuminating examples. Or maybe it's better to insult people. I don't know. It's a close call.

You have a habit of falling out with people on this mailing list. When someone disagrees with you about something, it might be better to try and read and understand where they are coming from, rather than arrogantly assuming from the outset that they can't possibly have a point. Some of my points you have just replied to with insults, suggesting you have no rebuttal to them. Your lack of self-awareness is mind-boggling. The problem is not everybody else.
Toby

On Friday 19 July 2024 at 06:11:52 BST, Michael Ossipoff <email9648742@gmail.com> wrote:  

On Wed, Jul 17, 2024 at 05:50 Toby Pereira tdp201b@yahoo.co.uk wrote:

Nice try, but I'm not the one making such sweeping claims about the method so do not need to define the conditions under which any claims about it hold.

I defined bias, & told how BF is completely unbiased twice at EM. Once when I introduced it in (I believe) 2006, & again in September’23.
No, you don’t have to define what conditions you’re talking about. But when someone can’t say what it is that they mean, it’s probably because they don’t know.

In any case, your "bias free" method certainly is not entirely unbiased without conditions as you claim. For one thing, by the measure that most people would reasonably see as the best measure of proportionality (the Sainte-Laguë measure), "bias free" favours small parties, so that in itself is a form of bias.

As I’ve surely mentioned, Toby hasn’t a clue what bias is. He’s continuing to confuse it with non-systematic departure from proportionality.

But even by that measure, it can quite clearly be shown that any deterministic method (that doesn't award fractional seats, and perhaps other obvious background caveats), can end up biased, depending on how votes are distributed in terms of small/large parties.

There, Toby is confusing the proportionality of a particular allocation with the bias of an allocation-rule.

It's pretty obvious in fact. And back in 2012, you seemed to acknowledge that assumptions were required, but it appears you've forgotten that now. http://lists.electorama.com/pipermail/election-methods-electorama.com//2012-July/095996.html

I’m not entirely sure what Toby is referring to. Warren Smith was making claims about what he felt was needed for defining, measuring & minimizing bias. I’ve never heard of anyone agreeing with him on that.
But, at first, I was willing to discuss how his requirements could be met.
But at least 1 or 2 academic journal papers reported about BF, & one named it the Ossipoff-Agnew method.
Agreement was expressed regarding its unbias.

It is not clear in any case that a method that balances small parties and large parties in this manner is better than one that gives a more mathematically proportional result. E.g. if you have two small parties and two large parties, and the two large parties end up slightly overrepresented and the two small parties underrepresented, this is not necessarily any worse than having one of each over/underrepresented.

Again, completely clueless about what bias is, & the difference between bias & non-systematic disproportionately.
Bias is worse, precisely because it consistently, systematically disfavors certain groups(large or small parties or states).
These things have all been explained to Toby several times, but he’s still reopening exactly the same blather as always.
Assertive, self-assured, & clueless.
In other words, the perfect poster-child for the Dunning-Kruger effect.

You just have four separate parties, two of which end up overrepresented and two under. There's no coalition between parties of similar size so this balancing is not required.

…demonstrating tha whenever it seems that Toby has surely maxed-out, he outdoes himself again.

Perhaps if you continue with your incorrect claims, I will have to block you!

Yes, if that will shut you up.

Toby

On Tuesday 16 July 2024 at 15:26:37 BST, Michael Ossipoff <email9648742@gmail.com> wrote:  

Oops!!! Toby forgot to say what conditions he was referring to. 
Bias-Free is entirely unbiased, without conditions.
I propose Saint-Lague (SL), because of its natural intuitive obviousness, & it’s near-unbias.
Bias-Free (BF) is a refinement that I’d offer as a possibility for later.
On Tue, Jul 16, 2024 at 06:04 Toby Pereira tdp201b@yahoo.co.uk wrote:

It is worth noting that the method Ossipoff declares to be "bias free" is only so under a very specific set of assumptions.
Toby
On Monday 15 July 2024 at 04:38:35 BST, Michael Ossipoff email9648742@gmail.com wrote:

There was interest in a poll about PR. But I feel that first the PR methods should be tried, used,  in a poll with the actual candidates & parties.
As I mentioned before, there’s no substitute for the experience of actually using the electoral methods in polls. You don’t know the methods until you use them.
So I propose a 3-part poll.  …presidential & PR:

1.  A Condorcet presidential-poll with 7 candidates + the approval-line. As others have mentioned, of course it could be counted by any rank-count that allows equal-ranking. But of course RP(wv) won here as the most collectively popular, & so its winner should be reported.
The approval-line of course would allow counting by methods that use explicit-approval.
…in addition to by the zero-cost implementation method.
2. A 3-seat STV poll among the same set of candidates as in the presidential-poll.
…as if we were electing a 3-person presidential triumvirate, or seats in some 3-member district in which those candidates are running.
Of course the STV rankings could be counted by any STV version, & integer STV is (in some ways) an easier count. But fractional STV is the unarbitrary STV that doesn’t require a rule or randomizing-process for the order in which ballots transfer.
Of course, because the STV doesn’t allow equal-rankin, then its ballots also could & would also be counted for an RCV count.
Of course if someone wanted to vote different rankings for STV & RCV, then they could write both & indicate which is which.
3. A 500-seat at-large party-PR allocation election. Of course voters vote for their favorite party, & seats are allocate to the parties in proportion to their votes.
Reported will be: allocations by:
Sainte-Lague, Bias-Free (Ossipoff-Agnew), d’Hondt, Largest-Remainder, & Huntington-Hill (“Equal-Proportions”).
SL & BF probably won’t differ from eachother.
————-
For the party-PR SL & BF allocation of 500 seats, the requirement for a party being seated 🪑 is about 1/7 of one percent of the vote.
For the 3-seat STV allocation, the requirement is being over 1/4 of the vote.
————-
SL, in actual implementations, requires .7 quotas for a party’s 1st seat. That’s to thwart, prevent & discourage splitting-strategy, which could otherwise sometimes be advantageous if the conditions were detected.
Because BF & SL give often the same allocation, then BF should have that same requirement.
That’s taken into account for the abovestated requirement for a party to be seated.
—————- 
Candidates for presidential & STV elections:
(These listings are alphabetical.)
Joe BidenRFK Jr.Chase OliverJill SteinDonald TrumpCornell WestMarianne Williamson approval-line——————————————Parties for party-PR election:
American Independent American Solidarity Constitution DemocratGreenLibertarian Peace & FreedomWorking Family —————Of course if this poll is going to happen, then additional nominations should be allowed. But we probably don’t need a week or two for that.Surely any additional nominations would be made within 2 days. So let’s say that the period for optional additional nominations ends exactly 48 hours after this message posts.
…& that the voting period begins at that same moment.
We don’t need a month for the voting-period, do we? Shall we say 1 week if there’s no electioneering, & 2 weeks if there’s electioneering?
Anyone can change any of their ballots during the voting period.————Of course if this poll happens, & if no one else volunteers to take the responsibility of recording the ballots, then I’ll do so.  …then of course will unblock the people I’ve blocked, for that purpose.————-It goes without saying that anything about the details of this poll could be objected-to, & then, if others support the objection, then discussion would be called-for. 
It’s always best to avoid the delay caused by a procedural vote, & so hopefully there will be a consensus agreement. …or at least it will be informally-obvious which position is supported or acceptable to the most people, based on opinions expressed.
An RP(wv) vote would be a reluctant last-resort. Anyone could call for it if consensus were adamantly refused & no position seemed to clearly have more support or acceptance.
Hopefully none of that will be necessary, but it’s good to have it mentioned for contingency.————-As the proposer of the poll, I should vote first, immediately at the beginning of the voting-period. I don’t know if anyone will participate, but, because there was participation in the previous poll, & because people have suggested a PR poll, & because there’s no substitute for using the electoral methods…then I’ll proceed on the assumption that there’s interest & that there might be participation.
If the poll doesn’t happen, it won’t be because I didn’t try to start it.

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

This back and forth probably isn't doing anyone any good, including those on the mailing list who may or may not be reading these messages. I found the paper "The Census and the Second Law: An Entropic Approach to Optimal Apportionment for the U.S. House of Representatives" by A.E. Charman found here: https://arxiv.org/abs/1712.09440 In the paper it says:
"With good marketing in mind, Ossipoff called this the “Bias-Free” (BF) Method. He was, however, not entirely clear regarding what was to be intended by this assertion, but it appears that he focused on a measure of bias assuming a uniform distribution of state populations, which seems quite questionable. But whatever his original motivation, by our analysis he does seem to have stumbled upon what, based on more fundamental grounds, we argue is the optimal method for apportionment, since this method is actually equivalent to the constrained global optimization of the relative entropy, as discussed in the main text."
Given what the paper says about the method, it would probably best best to take that as a win, but refer to the method in future as the Ossipoff-Agnew method, Method of Identric Means, or Entropic Apportionment (names the paper uses), rather than "Bias-Free".
Toby

On Saturday 20 July 2024 at 07:47:18 BST, Toby Pereira <tdp201b@yahoo.co.uk> wrote:  

You missed the point I was making that this isn't a single allocation, but that due to whatever reason, this is a stable population, so there is bias every election. And because we can't know a priori what distributions will be like in general, you might find that "bias free" does in fact favour small or large parties in the long term.
OK, what you actually said was "For one thing I doubt that they said that. It was known, at their time of writing, that SL has some (but very little) bias.
Maybe they said that SL is the only divisor-method ever having been used that is nearly unbiased. …or at least that it was the least biased of all divisor-methods that have been used."
I had put the relevant bit in quotes, because it was a quote not something for you to simply "doubt". When I later pressed this, nothing more was heard from you. Anyway, they said it was unbiased, not the least unbiased of those that currently exist, and you're now trying to claim that it was true at the time because it was the least unbiased. The mental gymnastics you're willing to go through.
Toby
On Saturday 20 July 2024 at 00:24:14 BST, Michael Ossipoff email9648742@gmail.com wrote:

On Fri, Jul 19, 2024 at 15:11 Toby Pereira tdp201b@yahoo.co.uk wrote:

I will actually give a very simple example of why the distribution of voters per party does matter and how no deterministic method can be guaranteed to pass Ossipoff's measure of unbias with no prior knowledge of the distribution.
Imagine you have a region with a stable and polarised electorate and 3/4 of the population always vote A, and 1/4 always vote B. And there are 5 seats on offer. You could give 3 seats to A and 2 to B, or 4 to A and 1 to B. A deterministic method will always give the same result, so whichever result the method picks, there will be a large or small party bias. A non-deterministic method could get round this though. Obviously Ossipoff could claim that this is a contrived distribution. Sure, but so is any distribution and you can't know a priori what distributions will be like in general. This is what I mean when I say that the "bias free" method relies on idealised conditions - conditions that aren't guaranteed in the real world.

Should we laugh or cry?
In Toby’s example, SL, BF, DH & EP (HH) all give the following seat-allocation:
A: 4B: 1
What’s this?!  B should get 1/4 of the seats, but it only gets 1/5!
Bias!!!
Actually, no. As I said, Toby hasn’t a clue what bias is.
As I carefully explained to Toby in the message that he’s “replying to”, bias is systematic, consistent disfavor, in s/v.
Therefore, bias is NOT disproportion in a particular allocation.
The abovestated allocation has DISPROPORTION. 
But, by definition, only an allocation-rule, & NOT a particular allocation, can have bias.
Toby keeps repeating his blather, completely obliviously to what has been explained to him.
Dunning-Kruger is vindicated & demonstrated again!

One last point - when I talk about Sainte-Laguë being the best measure of proportionality, I have previously quoted Balinski and Peyton Young on this where they say:
"Webster's is the unique unbiased divisor method. It seems amazing therefore that Hill's method could have been chosen in 1941 on precisely the ground that it was the unbiased method, and that Webster's method was discarded."which Ossipoff has ignored.

I didn’t ignore it. I merely pointed out that you’re misinterpreting what he meant.
At the time when he said that, BF didn’t exist as an allocation-rule proposal. So, what he said was true at the time when he said it.
Arguably it could be said now too, if the statement is understood to encompass only those allocation-rules that have been used for PR or apportionment.
Among the divisor-methods that have ever been used, SL is the most unbiased & the only one remotely unbiased.
HH/EP is about twice as biased as SL.

On Friday 19 July 2024 at 10:26:28 BST, Toby Pereira <tdp201b@yahoo.co.uk> wrote:  

I will reply in one block rather than line-by-line, as it might become a bit of a mess.
If you are defining a specific sort of bias, you need to reiterate it in every post you use the term, or at least in every discussion thread. "Bias" is already a word in the English language and you do not have a monopoly over it. The form of bias I was talking about was systemic departure from proportionality in favour of small parties, not non-systemic as you dishonestly or ignorantly claim. I have been quite clear about this. I have also explained at length why Sainte-Laguë is the single most reasonable measure of proportionality and not just any old allocation rule.
What I was referring to in your post about originally accepting that assumptions were required was when you put "If it is equally likely to find a party with its final quotient anywhere in interval N". Note the "if". This seemed to be the assumption that your unbiased method was dependent on. Is it not then?
I've never doubted that your method has interesting theoretical properties under idealised conditions, but when you put things like "Bias-Free is entirely unbiased, without conditions", you're claiming too much and it's simply wrong.
You could even demonstrate to people on this list how your method is unbiased, or provide a link to where you have done so, perhaps with some illuminating examples. Or maybe it's better to insult people. I don't know. It's a close call.

You have a habit of falling out with people on this mailing list. When someone disagrees with you about something, it might be better to try and read and understand where they are coming from, rather than arrogantly assuming from the outset that they can't possibly have a point. Some of my points you have just replied to with insults, suggesting you have no rebuttal to them. Your lack of self-awareness is mind-boggling. The problem is not everybody else.
Toby

On Friday 19 July 2024 at 06:11:52 BST, Michael Ossipoff <email9648742@gmail.com> wrote:  

On Wed, Jul 17, 2024 at 05:50 Toby Pereira tdp201b@yahoo.co.uk wrote:

Nice try, but I'm not the one making such sweeping claims about the method so do not need to define the conditions under which any claims about it hold.

I defined bias, & told how BF is completely unbiased twice at EM. Once when I introduced it in (I believe) 2006, & again in September’23.
No, you don’t have to define what conditions you’re talking about. But when someone can’t say what it is that they mean, it’s probably because they don’t know.

In any case, your "bias free" method certainly is not entirely unbiased without conditions as you claim. For one thing, by the measure that most people would reasonably see as the best measure of proportionality (the Sainte-Laguë measure), "bias free" favours small parties, so that in itself is a form of bias.

As I’ve surely mentioned, Toby hasn’t a clue what bias is. He’s continuing to confuse it with non-systematic departure from proportionality.

But even by that measure, it can quite clearly be shown that any deterministic method (that doesn't award fractional seats, and perhaps other obvious background caveats), can end up biased, depending on how votes are distributed in terms of small/large parties.

There, Toby is confusing the proportionality of a particular allocation with the bias of an allocation-rule.

It's pretty obvious in fact. And back in 2012, you seemed to acknowledge that assumptions were required, but it appears you've forgotten that now. http://lists.electorama.com/pipermail/election-methods-electorama.com//2012-July/095996.html

I’m not entirely sure what Toby is referring to. Warren Smith was making claims about what he felt was needed for defining, measuring & minimizing bias. I’ve never heard of anyone agreeing with him on that.
But, at first, I was willing to discuss how his requirements could be met.
But at least 1 or 2 academic journal papers reported about BF, & one named it the Ossipoff-Agnew method.
Agreement was expressed regarding its unbias.

It is not clear in any case that a method that balances small parties and large parties in this manner is better than one that gives a more mathematically proportional result. E.g. if you have two small parties and two large parties, and the two large parties end up slightly overrepresented and the two small parties underrepresented, this is not necessarily any worse than having one of each over/underrepresented.

Again, completely clueless about what bias is, & the difference between bias & non-systematic disproportionately.
Bias is worse, precisely because it consistently, systematically disfavors certain groups(large or small parties or states).
These things have all been explained to Toby several times, but he’s still reopening exactly the same blather as always.
Assertive, self-assured, & clueless.
In other words, the perfect poster-child for the Dunning-Kruger effect.

You just have four separate parties, two of which end up overrepresented and two under. There's no coalition between parties of similar size so this balancing is not required.

…demonstrating tha whenever it seems that Toby has surely maxed-out, he outdoes himself again.

Perhaps if you continue with your incorrect claims, I will have to block you!

Yes, if that will shut you up.

Toby

On Tuesday 16 July 2024 at 15:26:37 BST, Michael Ossipoff <email9648742@gmail.com> wrote:  

Oops!!! Toby forgot to say what conditions he was referring to. 
Bias-Free is entirely unbiased, without conditions.
I propose Saint-Lague (SL), because of its natural intuitive obviousness, & it’s near-unbias.
Bias-Free (BF) is a refinement that I’d offer as a possibility for later.
On Tue, Jul 16, 2024 at 06:04 Toby Pereira tdp201b@yahoo.co.uk wrote:

It is worth noting that the method Ossipoff declares to be "bias free" is only so under a very specific set of assumptions.
Toby
On Monday 15 July 2024 at 04:38:35 BST, Michael Ossipoff email9648742@gmail.com wrote:

There was interest in a poll about PR. But I feel that first the PR methods should be tried, used,  in a poll with the actual candidates & parties.
As I mentioned before, there’s no substitute for the experience of actually using the electoral methods in polls. You don’t know the methods until you use them.
So I propose a 3-part poll.  …presidential & PR:

1.  A Condorcet presidential-poll with 7 candidates + the approval-line. As others have mentioned, of course it could be counted by any rank-count that allows equal-ranking. But of course RP(wv) won here as the most collectively popular, & so its winner should be reported.
The approval-line of course would allow counting by methods that use explicit-approval.
…in addition to by the zero-cost implementation method.
2. A 3-seat STV poll among the same set of candidates as in the presidential-poll.
…as if we were electing a 3-person presidential triumvirate, or seats in some 3-member district in which those candidates are running.
Of course the STV rankings could be counted by any STV version, & integer STV is (in some ways) an easier count. But fractional STV is the unarbitrary STV that doesn’t require a rule or randomizing-process for the order in which ballots transfer.
Of course, because the STV doesn’t allow equal-rankin, then its ballots also could & would also be counted for an RCV count.
Of course if someone wanted to vote different rankings for STV & RCV, then they could write both & indicate which is which.
3. A 500-seat at-large party-PR allocation election. Of course voters vote for their favorite party, & seats are allocate to the parties in proportion to their votes.
Reported will be: allocations by:
Sainte-Lague, Bias-Free (Ossipoff-Agnew), d’Hondt, Largest-Remainder, & Huntington-Hill (“Equal-Proportions”).
SL & BF probably won’t differ from eachother.
————-
For the party-PR SL & BF allocation of 500 seats, the requirement for a party being seated 🪑 is about 1/7 of one percent of the vote.
For the 3-seat STV allocation, the requirement is being over 1/4 of the vote.
————-
SL, in actual implementations, requires .7 quotas for a party’s 1st seat. That’s to thwart, prevent & discourage splitting-strategy, which could otherwise sometimes be advantageous if the conditions were detected.
Because BF & SL give often the same allocation, then BF should have that same requirement.
That’s taken into account for the abovestated requirement for a party to be seated.
—————- 
Candidates for presidential & STV elections:
(These listings are alphabetical.)
Joe BidenRFK Jr.Chase OliverJill SteinDonald TrumpCornell WestMarianne Williamson approval-line——————————————Parties for party-PR election:
American Independent American Solidarity Constitution DemocratGreenLibertarian Peace & FreedomWorking Family —————Of course if this poll is going to happen, then additional nominations should be allowed. But we probably don’t need a week or two for that.Surely any additional nominations would be made within 2 days. So let’s say that the period for optional additional nominations ends exactly 48 hours after this message posts.
…& that the voting period begins at that same moment.
We don’t need a month for the voting-period, do we? Shall we say 1 week if there’s no electioneering, & 2 weeks if there’s electioneering?
Anyone can change any of their ballots during the voting period.————Of course if this poll happens, & if no one else volunteers to take the responsibility of recording the ballots, then I’ll do so.  …then of course will unblock the people I’ve blocked, for that purpose.————-It goes without saying that anything about the details of this poll could be objected-to, & then, if others support the objection, then discussion would be called-for. 
It’s always best to avoid the delay caused by a procedural vote, & so hopefully there will be a consensus agreement. …or at least it will be informally-obvious which position is supported or acceptable to the most people, based on opinions expressed.
An RP(wv) vote would be a reluctant last-resort. Anyone could call for it if consensus were adamantly refused & no position seemed to clearly have more support or acceptance.
Hopefully none of that will be necessary, but it’s good to have it mentioned for contingency.————-As the proposer of the poll, I should vote first, immediately at the beginning of the voting-period. I don’t know if anyone will participate, but, because there was participation in the previous poll, & because people have suggested a PR poll, & because there’s no substitute for using the electoral methods…then I’ll proceed on the assumption that there’s interest & that there might be participation.
If the poll doesn’t happen, it won’t be because I didn’t try to start it.

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