[EM] Unified Majority electoral system

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[EM] Unified Majority electoral system

John
[Not subscribed, so please CC me replies]

I'm pushing two new pieces of political science, as far as I can tell. One is about representation structure, and the other is about elections.

On representation structure, I've been suggesting bicameral legislatures with a single-seat (Senate) and a multi-seat (House) component.  Senates are overall representation, while the House becomes a proportionally-representative institution with more-individualized voices.

This all stands on an electoral system called Unified Majority.


Let's run through history.

The United States once primarily nominated by party caucus.  Party central committees would select their own representatives and put them up for the voters to elect in the general election.

The rise of the Party Primary put more control in the hands of the electorate, allowing voters registered to the Party—party members—to nominate directly.  Focus shifted to candidates rather than parties, solidifying the two-plus party system.

Even so, the two parties are the Democrats and the Republicans, and whichever gets the most votes gets their candidate out front.  Primaries only represent the voters actually voting, and party-line voters have less marginal utility than activist voters, so the Party Primary tends to draw representation for a surprisingly-small minority.

Unified Majority changes this.

Unified Majority uses Single Transferable Vote in a nonpartisan blanket primary.  For a single-winner election, it nominates five or seven; for a multi-winner election, it nominates twice the number of ultimate winners.  If there are fewer candidates, no primary occurs.

A single-winner election completes with a Condorcet vote, notably Tideman's Alternative Method; while multi-winner elections use STV.

Parties represent platforms, and a variation in party ideology can result in multiple nominations from the same party under Unified Majority.  The Condorcet single-winner represents the center of this ideological span, thus the overall consensus.

Data suggests voters will rank six candidates fairly reliably, and then rapidly drop off.

A single-winner ranked election between an odd number not exceeding twice as many candidates should find the Condorcet winner.  With eleven candidates, voters should largely rank up to the center candidate.  Fewer candidates improves on this:  excluding bullet-voters, a five-candidate election ensures the most-extreme voters will overlap the center by ranking merely three candidates; for seven, it's four.

Likewise, this overlap tends to enhance STV in large fields of candidates.  A voter centered between two candidates will reach at least three candidates to their preferred direction if ranking six.  The Nonpartisan Blanket Primary can thus easily include six times the ultimate nominees—for seven nominees, that's 42 candidates.

This explains the reason for a primary.

My preferred STV system is Meek-STV, although I'm uncertain how that really compares to Warren-STV.  My experiments suggest Meek-STV will always elect a candidate representing the Droop quota:  if electing 3 and 25% of the population ranks some subset of candidates above all candidates ranked first, second, and third by the other 75% of the population, then the 25% will determine their own candidate.

I have considered a more-convoluted measure:

 - Run STV;
 - Replace the final winner with a Condorcet candidate computed from all ballots with their final weights (including weight at exhaustion), excluding the winning candidates.

Largely, I have problems with the early-elimination issue in STV, and have considered tweaks like restarting the count from the top after each win, accounting for the weights of the ballots and excluding the winning candidates (this will work with Warren, but not Meek).

Unified Majority with Meek-STV/Tideman's Alternative has a few interesting features:

 - It represents the span of the electorate's ideology, rather than parties, in the General;
 - It is immune to gerrymandering;
 - It is immune to tactical nomination for MANY reasons;
 - It maximizes the likelihood of actually finding and electing the Condorcet candidate when given a large number of candidates.

Unified Majority multi-winner is only really necessary for (n) winners with (6n) candidates, in theory, but drawing down to (2n) makes me more comfortable that we're not losing voters who vote for 2-3 candidates who are ultimately losers and thus get their ballots exhausted.

Thoughts?

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Re: [EM] Unified Majority electoral system

Kristofer Munsterhjelm-3
On 04/02/2019 01.02, John wrote:

> [Not subscribed, so please CC me replies]
>
> I'm pushing two new pieces of political science, as far as I can tell.
> One is about representation structure, and the other is about elections.
>
> On representation structure, I've been suggesting bicameral legislatures
> with a single-seat (Senate) and a multi-seat (House) component.  Senates
> are overall representation, while the House becomes a
> proportionally-representative institution with more-individualized voices.
>
> This all stands on an electoral system called Unified Majority.
>
> https://www.nordicmodelusa.org/policy/government-and-representation/elections/unified-majority-elections/

Not bad; one could definitely do worse than such a primary.

As I said to Rob Lanphier when he was asking about MAF, I would suggest
that the candidates who go on to the general always include the winner
of the single-winner election based on the primary ballots. That is, if
you're using Tideman's Alternative Smith, then it would be better to
have an even number of candidates plus the Alternative Smith winner,
than an odd number of candidates.

Two reasons for this: First, this makes the primary+general system no
worse than if there were no primary to begin with. If the voters behave
identically in both rounds, then the single-winner method's choice is
preserved through both rounds.

Second, the logic of STV is ultimately the same logic as that of IRV. I
imagine the reason you propose an odd number is that if the left and
right wings are roughly equally strong, then there will be a center
candidate for that last spot; but STV will use IRV to populate the last
spot (after the deweighting for each wing roughly cancels out). And IRV
has a problem with center squeeze in such situations.

You could get the same effect by using your more convoluted measure, but
just augmenting an even group with the single-method winner is easier
and gives the same result when the wings are balanced.

> Let's run through history.
>
> The United States once primarily nominated by party caucus.  Party
> central committees would select their own representatives and put them
> up for the voters to elect in the general election.
>
> The rise of the Party Primary put more control in the hands of the
> electorate, allowing voters registered to the Party—party members—to
> nominate directly.  Focus shifted to candidates rather than parties,
> solidifying the two-plus party system.
>
> Even so, the two parties are the Democrats and the Republicans, and
> whichever gets the most votes gets their candidate out front.  Primaries
> only represent the voters actually voting, and party-line voters have
> less marginal utility than activist voters, so the Party Primary tends
> to draw representation for a surprisingly-small minority.
>
> Unified Majority changes this.
>
> Unified Majority uses Single Transferable Vote in a nonpartisan blanket
> primary.  For a single-winner election, it nominates five or seven; for
> a multi-winner election, it nominates twice the number of ultimate
> winners.  If there are fewer candidates, no primary occurs.
>
> A single-winner election completes with a Condorcet vote, notably
> Tideman's Alternative Method; while multi-winner elections use STV.
>
> Parties represent platforms, and a variation in party ideology can
> result in multiple nominations from the same party under Unified
> Majority.  The Condorcet single-winner represents the center of this
> ideological span, thus the overall consensus.
>
> Data suggests voters will rank six candidates fairly reliably, and then
> rapidly drop off.
>
> A single-winner ranked election between an odd number not exceeding
> twice as many candidates should find the Condorcet winner.  With eleven
> candidates, voters should largely rank up to the center candidate. 
> Fewer candidates improves on this:  excluding bullet-voters, a
> five-candidate election ensures the most-extreme voters will overlap the
> center by ranking merely three candidates; for seven, it's four.
>
> Likewise, this overlap tends to enhance STV in large fields of
> candidates.  A voter centered between two candidates will reach at least
> three candidates to their preferred direction if ranking six.  The
> Nonpartisan Blanket Primary can thus easily include six times the
> ultimate nominees—for seven nominees, that's 42 candidates.
>
> This explains the reason for a primary.
>
> My preferred STV system is Meek-STV, although I'm uncertain how that
> really compares to Warren-STV.  My experiments suggest Meek-STV will
> always elect a candidate representing the Droop quota:  if electing 3
> and 25% of the population ranks some subset of candidates above all
> candidates ranked first, second, and third by the other 75% of the
> population, then the 25% will determine their own candidate.

STV in general meets the Droop proportionality criterion, which states
that if more than k Droop quotas' worth of voters rank m candidates
ahead of everybody else (not necessarily in the same order), then min(k,
m) of these must be elected.

As for Meek and Warren, when I did some proportionality simulations long
ago, those two methods were very close, so I'd say that there's little
difference between the two. The main reason for choosing one over the
other is if you prefer additive weights over multiplicative ones (in
which case choose Warren), or the other way around (in which case choose
Meek).

> I have considered a more-convoluted measure:
>
>  - Run STV;
>  - Replace the final winner with a Condorcet candidate computed from all
> ballots with their final weights (including weight at exhaustion),
> excluding the winning candidates.
>
> Largely, I have problems with the early-elimination issue in STV, and
> have considered tweaks like restarting the count from the top after each
> win, accounting for the weights of the ballots and excluding the winning
> candidates (this will work with Warren, but not Meek).

You could use Bucklin transferable vote instead of STV. Basically, you
do a Bucklin election and whenever a candidate who's not yet elected
exceeds the quota, you elect him and reweight the ballots.

This will mitigate the early-elimination problem because BTV doesn't
eliminate any candidates. On the other hand, it doesn't have the kind of
record of former use that STV has.

A Condorcet-STV hybrid like CPO-STV or Schulze STV would entirely
eliminate the problem. Unfortunately, they're way too convoluted and
generally take time proportional to some power of the number of possible
outcomes, which is rather hairy when that number is 42 choose 7.

> Unified Majority with Meek-STV/Tideman's Alternative has a few
> interesting features:
>
>  - It represents the span of the electorate's ideology, rather than
> parties, in the General;
>  - It is immune to gerrymandering;
>  - It is immune to tactical nomination for MANY reasons;

Strictly speaking, STV is not independent of clones; see
http://www.votingmatters.org.uk/ISSUE3/P5.HTM. So there is one way that
it's not immune to tactical nomination, although it is probably fairly
resistant since the single-winner method is independent of clones.

(BTV would not be independent of clones either. I'm not aware of any
proportional multiwinner method that is.)

>  - It maximizes the likelihood of actually finding and electing the
> Condorcet candidate when given a large number of candidates.
>
> Unified Majority multi-winner is only really necessary for (n) winners
> with (6n) candidates, in theory, but drawing down to (2n) makes me more
> comfortable that we're not losing voters who vote for 2-3 candidates who
> are ultimately losers and thus get their ballots exhausted.
>
> Thoughts?
>
> ----
> Election-Methods mailing list - see http://electorama.com/em for list info
>

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Re: [EM] Unified Majority electoral system

John


On Thu, Feb 7, 2019 at 5:01 PM Kristofer Munsterhjelm <[hidden email]> wrote:
On 04/02/2019 01.02, John wrote:
> [Not subscribed, so please CC me replies]
>

 
As I said to Rob Lanphier when he was asking about MAF, I would suggest
that the candidates who go on to the general always include the winner
of the single-winner election based on the primary ballots. That is, if
you're using Tideman's Alternative Smith, then it would be better to
have an even number of candidates plus the Alternative Smith winner,
than an odd number of candidates.

Two reasons for this: First, this makes the primary+general system no
worse than if there were no primary to begin with. If the voters behave
identically in both rounds, then the single-winner method's choice is
preserved through both rounds.


Doesn't actually work.

We've found that voters reliably rank up to six, then drop off rapidly.  If you have 7 candidates, just have your general election and no primary; but what if you have, say, 30?

AAAAAA BBBBBB CCCCCC DDDDDD EEEEEE

Thirty candidates in groups of six.  Assuming they're evenly distributed ideologically (they're not), voters will elect the center of these groups, roughly, under STV.

What about under a Condorcet system?

You wind up with voters grouping around A, B, C, D, or E span.  The largest group elects the Condorcet candidate among that group.  If your largest group is the D-span voters, you get the condorcet for D.  You may get something between C-D or D-E as an actual candidate span.

While STV will fail this way if near-exclusively A and A-B voters and only E and E-D voters show up to the primary, it will still tend to elect from the span A, B, C, D, and E if 1/6 of the voters are in each span.  Moreover, you're more-likely to get overlap toward the center, and there's a greater population in the mean and so 2% lower turn-out among that population doesn't correlate to 2% lower total votes in that area.

So if your span is 22, 21, 17, 19, 21, your Condorcet candidate will tend to be someone around A to A-B.

Your five STV candidates will be somewhere around the middle of A, B, C, D, and E.
 
Second, the logic of STV is ultimately the same logic as that of IRV. I
imagine the reason you propose an odd number is that if the left and
right wings are roughly equally strong, then there will be a center
candidate for that last spot; but STV will use IRV to populate the last
spot (after the deweighting for each wing roughly cancels out). And IRV
has a problem with center squeeze in such situations.

In a field with a large number of candidates, the span across the center will be full of similar candidates.
 
You could get the same effect by using your more convoluted measure, but
just augmenting an even group with the single-method winner is easier
and gives the same result when the wings are balanced.


Only if you assume all voters rank all the way to the Condorcet candidate.  If voters tend to rank substantially-fewer, then you get what is conceptually-similar to a Plurality winner among the usual STV results.


>
> My preferred STV system is Meek-STV, although I'm uncertain how that
> really compares to Warren-STV.  My experiments suggest Meek-STV will
> always elect a candidate representing the Droop quota:  if electing 3
> and 25% of the population ranks some subset of candidates above all
> candidates ranked first, second, and third by the other 75% of the
> population, then the 25% will determine their own candidate.

STV in general meets the Droop proportionality criterion, which states
that if more than k Droop quotas' worth of voters rank m candidates
ahead of everybody else (not necessarily in the same order), then min(k,
m) of these must be elected.


Good to know. 

As for Meek and Warren, when I did some proportionality simulations long
ago, those two methods were very close, so I'd say that there's little
difference between the two. The main reason for choosing one over the
other is if you prefer additive weights over multiplicative ones (in
which case choose Warren), or the other way around (in which case choose
Meek).

Nice.  Which is simpler to implement? ;)

> I have considered a more-convoluted measure:
>
>  - Run STV;
>  - Replace the final winner with a Condorcet candidate computed from all
> ballots with their final weights (including weight at exhaustion),
> excluding the winning candidates.
>
> Largely, I have problems with the early-elimination issue in STV, and
> have considered tweaks like restarting the count from the top after each
> win, accounting for the weights of the ballots and excluding the winning
> candidates (this will work with Warren, but not Meek).

You could use Bucklin transferable vote instead of STV. Basically, you
do a Bucklin election and whenever a candidate who's not yet elected
exceeds the quota, you elect him and reweight the ballots.

This will mitigate the early-elimination problem because BTV doesn't
eliminate any candidates. On the other hand, it doesn't have the kind of
record of former use that STV has.


Bucklin is also highly-susceptible to strategy and can be manipulated by bullet voting.
 
A Condorcet-STV hybrid like CPO-STV or Schulze STV would entirely
eliminate the problem. Unfortunately, they're way too convoluted and
generally take time proportional to some power of the number of possible
outcomes, which is rather hairy when that number is 42 choose 7.


Schulze STV would be awesome.
 
> Unified Majority with Meek-STV/Tideman's Alternative has a few
> interesting features:
>
>  - It represents the span of the electorate's ideology, rather than
> parties, in the General;
>  - It is immune to gerrymandering;
>  - It is immune to tactical nomination for MANY reasons;

Strictly speaking, STV is not independent of clones; see
http://www.votingmatters.org.uk/ISSUE3/P5.HTM. So there is one way that
it's not immune to tactical nomination, although it is probably fairly
resistant since the single-winner method is independent of clones.


True, although Hare is fairly resistant in that it's more likely to select one of the clones than Plurality.  Adding a clone can eliminate a third candidate and elect a fourth, rather than eliminating the candidate being cloned.

These things become less-likely with larger primaries, and you can just skip the primary with 7 candidates.  The 2016 election was half a dozen Republicans, three Democrats, a Libertarian, a Green, an Independent, and a few others who showed up somehow.  That's over a dozen.

That's a practical matter; it's always technically-vulnerable.
 
> ----
> Election-Methods mailing list - see http://electorama.com/em for list info
>


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