[EM] Challenge: two-party methods

[Kristofer Munsterhjelm]

Juho Laatu wrote:
> On 9.7.2011, at 14.23, Kristofer Munsterhjelm wrote:
> 
>> Juho Laatu wrote:
>>> After some recent discussions and thoughts around two-party
>>> systems I thought it would be interesting to discuss two-party
>>> systems also in a more positive spirit. The assumption is thus
>>> that we want the system to be two-party oriented. We want to have
>>> two strong parties, and one of them should rule. We want to allow
>>> only well established parties with wide support to rule. The
>>> first obvious approach is to ban all other parties than the two
>>> leading parties. But maybe we don't want  to be so brutal. Let's
>>> not ban the possibly already existing, much liked and hopeful
>>> third parties. It is also good to have some competition in the
>>> system. Let's not allow the two leading parties think that they
>>> don't have to care about the voters and they can do whatever they
>>> want, and stay in power forever. What would be a good such
>>> method? In addition to what was already said we surely want e.g.
>>> to avoid the classical spoiler problems.
>> I can think of two simple PR-based methods.
>> 
>> In the first, you use ordinary divisor-based PR, but set the
>> divisors so that they have a great large-party bias (even worse
>> than D'Hondt).
> 
> It seems that this method would favour large parties so that they
> would get lots of seats, and it would make sense to generally vote
> for them. One problem with respect to the targets might be that small
> parties may have problems to grow since votes to them have less
> weight than votes to large parties. If left wing gets 50% of the
> votes, and in the right wing there are two parties, 35% and 15%, then
> left wing gets majority. The small party was a spoiler to the right
> wing.

It's relatively simple to get around such troubles: just slap an Asset
patch on it. For that matter, you could have Asset with the requirement
that the negotiations don't end until one of the parties has greater
than a majority of the assets.

>> In the second, you also use ordinary divisor-based PR, but top up
>> the list of the largest party so that it always gets 50%+1 of the
>> seats if it would otherwise get below that.
> 
> It seems that also here we may have a spoiler problem. In situation
> 40: L1, 10: L2, 40: R1, 10: R2 any additional voters moving from a
> 40% group to the 10% group of the same wing would be spoilers.

Same response :-)

If you want to deal directly with the spoiler problem, you'd need a
method that has the property that it grants every party a score, and
that cloning groups of parties gives one of the group of parties (since
the method can't know which are clones) the same score as the original
party would have if there was no cloning.

>> But I think that any two-party system will discourage smaller
>> parties. If only the two major parties can rule, voters will
>> strategically think that "either I can use my vote to grant the
>> lesser evil more seats/power so it can defeat the greater evil, or
>> I can use my vote to vote for a small party that hasn't got a
>> chance beyond being the opposition anyway. I'll do the former".
>> That sort of thinking will create an invisible barrier to third
>> parties, because as long as the third parties aren't large enough
>> that they might win (become one of the top two) with a small amount
>> of additional votes, voters won't vote for them, and if they don't
>> vote for them, they'll never get close enough to the threshold.
> 
> There might be irrational fears, that may be based on how the old
> methods have worked. The target is anyway to make such fears
> irrational. The intention is that although my favourite small party
> can not win this election, it is quite possible that it will win in
> the next election, or one after that.
> 
> Even If the votes are now 50: A, 45: B>C>A, 5: C>B>A, next time they
> could be 50: A, 35: B>C>A, 15: C>B>A, and next time 50: A, 24: B>C>A,
> 26: C>B>A. C should thus be able to grow without disturbing the
> balance between A and {B, C}. (These votes should work in the method
> that I proposed.)

That could work, if there was some way of measuring support so that 
voters of minor parties could see that they're helping the minor party 
get closer to major status. However, if the measure of support is the 
number of seats, then either a vote gives a major party another seat (or 
the ability to get past the threshold), or the vote gives a minor party 
the ability to get past the threshold.

You could then say that if there's an effective seat barrier (the 
threshold) so that minor parties don't *get* any more seats until 
they're at major party status, then voting for the minor party first 
won't harm your vote if that vote doesn't lead to the minor party 
getting more seats, because then your vote can help your major party 
instead; and the minor party can't get seats before it's at major party 
status, so your vote isn't harming your major party until the point 
where it would help the minor party more than it harms the major party. 
This kind of logic is similar to that in Condorcet methods, (assuming 
CW, etc), you don't really risk anything by putting Nader first, because 
either Nader is elected, in which case that's what you wanted, or he's 
not, which means your vote will help elect Gore instead of Bush.

That reasoning itself is sound enough, but I still think it would need 
some sort of "contingent score", so that people who vote the minor party 
first can see that the minor party is increasing in support, even if 
that support doesn't give them seats. If the voters are under a time 
constraint, then voters who would otherwise not bother to consider the 
third parties might, once they see that one of them is getting close to 
becoming a major party.

>> I can think of two ways to get around that, but both would bend the
>> definition of a two-party system.
>> 
>> Let's call the first an "explicit coalition system". The election
>> process itself is party list PR. After the election is done, a
>> group of parties with a total vote share greater than a majority
>> must form a coalition; they do so by an internal supermajority
>> vote, after which this group gets the government and the rest
>> becomes the opposition. After that is done, they rule until at
>> least one of the parties (or some fraction of the whole group),
>> plus the opposition (or supermajority thereof), agrees to dissolve
>> the current coalition. After that is done, there are new elections.
>> The current coalition rules until the next coalition can organize
>> itself.
> 
> Are you saying that actually many multi-party systems (that work
> pretty much in the described way) are actually single-party
> governments, and therefore the system is essentially a government vs.
> opposition system, and that would make it effectively a two-party
> system? It is true that governments typically have a unified policy,
> and the opposition takes the opposite position. Technically this
> approach meets the two targets that I set, but I was thinking of
> somewhat more stable parties, not ones that would be redesigned after
> every election based on the results that the numerous smaller parties
> that participate in the election do get :-).

It's a more hardened version of a coalition. Note that there are no 
minority governments in that system: the government has to be led by a 
coalition. Furthermore, the coalition isn't very loose: it has to stay 
together to remain in power, and the parties can't be released from the 
coalition in contentious matters. All of these aspects make it less a 
coalition in the PR sense and more a single party - a metaparty that 
consists of the parties in the coalition.

 From the actions of the current coalition in Norway, the coalition 
being quite "hard" in that sense, I don't think this sort of system 
would be preferable to pure PR, but it might be better than R-and-D 
party-leadership type two-party systems. (Then again, I also think that 
this is more or less an intellectual exercise: I wouldn't want a 
two-party structure in the first place, and if you had an electorate 
that did, you could just use an ordinary representative system since the 
voters would vote to preserve the two-party system, like in Malta.)

> (Note that I wrote the targets for a single-winner election (they
> talk about electing one of the candidates) and we have now expanded
> the discussion also to multi-winner elections. They are
> interchangeable though, since many single seats van be summed up to
> multiple seats, and multiple representatives can elect a single
> winner, maybe a government coalition or a president.)

I think it's simpler to consider party list PR methods than STV-type 
ones since party list can go directly to parties and give different 
winners different power. Then, if it is required, one can go from the PR 
methods to the STV-methods later, trying to find out how to embody the 
same logic in a more complex system.

>> The second, I'd call "PR by credit". Again, votes are counted as in
>> party list. Each party also has an "account". After the election,
>> the number of votes for each party is added to the relevant party's
>> account. Then the parties allocate votes to gain seats in a
>> continuous bidding process. That is, call parties 1...n's current
>> bids, B_1...B_n. Then the tentative seats allocation is according
>> to some major-party biased divisor method that considers B_1...B_n
>> the number of votes each party got. The seats count is updated
>> continuously until the timeout, then each party's bid is withdrawn
>> from its account. While it is unfair in any given election, the
>> smaller parties can accumulate votes in their accounts and later
>> use this to take the throne of government, if for only a term. 
>> However, I think this kind of hybrid monetary system would have
>> some adverse results. First, it would cause great oscillations. The
>> composition of the parliament could swing hard left, with lots of,
>> say, environmental bills, then swing hard right, with the new
>> government scrambling to undo those bills and to impose their own,
>> then swing hard left again, each sweep of the pendulum causing
>> chaos. Second, differences in turnout could add more noise: if
>> there's less turnout, there's less of an impact to each party's
>> account.
> 
> I think two-party countries typically oscillate between two extremes.
> Or actually they are not extremes since both major parties tend to
> move close to each others in the hope of making some of the voters of
> the other party to move on their side. But oscillation of one-party
> governments tends to be the rule. Although in multi-party systems
> governments tend to be "compromise based combined governments" we
> need not follow that rule in our two-party system.

True, but I don't think it's a good way of governing :-) Say you're 
driving a car, and you turn the steering wheel to the left until the 
left of your car is at the middle of the road. Then you turn your 
steering wheel right until the right side of your car is at the edge of 
the road. Then you turn left again... sure, the mean position of your 
car will be in the middle of your lane, but I don't think your 
passengers would be very happy if you drove that way.

The median voter theorem might moderate the amplitude of the direction 
changes, but it is not absolute, since the Republican and Democratic 
parties do indeed differ. Someone (I don't remember who, but it might 
have been Warren) argued that the conflict between the median voter 
theorem (that means the two parties have to be similar) and the parties' 
desire to seek their own way meant that they essentially had to lie to 
the voters: seem more centrist than they really were. If that's true, 
that's not a desirable property, either.

> This kind of oscillation and also credit based methods typically
> offer proportionality in time (instead of "proportionality now" as
> multi-party parliaments or governments). I'll propose one additional
> method to explain what I mean and how this relates to the interest of
> letting only the major parties rule.
> 
> Let's say that the votes are approval votes. All parties have credit
> accounts that contain unused ballots from the previous elections. The
> votes of this election will be added to the credit accounts. The
> winner is the party with most credit ballots. We will delete as many
> ballots from that party as there are voters (total number of voters)
> (some fine-tuning may be needed because the number of voters may
> change between elections). Note that we deleted actual ballots, i.e.
> also those other parties that were approved in some of these ballots
> lost some ballots from their account. Maybe we will subtract votes
> proportionally so that ballots with different approval patterns will
> be reduced in same proportion (some fine-tuning maybe here too, maybe
> all ballots to this party only will be eliminated).

Obviously (as you've discovered), you can't just store the Approval 
counts for each party in the party's account. That would lead to a 
significant teaming problem where a party makes ten clones and then 
whenever the main party wins, the clones can win the next ten terms. (It 
gets worse with an Asset patch.) So you have to remove actual ballots 
when you remove votes, as you've mentioned. However, that could lead to 
rather strange outcomes.

Say that there were some voters in term t who voted both left and right. 
Then in term t+1, the right party decides to use some of its credit. 
Would that then also decrease the left party's credit (because of the 
votes from term t)? If not, then teaming is possible, otherwise, it's 
possible to add noise to the credit by having party voters also vote for 
another party, and then just removing those ballots later on.

> Now we have a system that puts one party at a time in power. It is
> fully proportional in time in the sense that all parties will get
> their time in office one day. But if we want to stop small parties
> winning the election unless they grow into large parties we need some
> additional rules. One could for example allow only parties that have
> reached some predetermined number of votes in this election to win
> (or...). We could also eliminate votes that are older than five
> elections. There are also other tricks (fine-tuning and more coarse
> tuning possible again).

That's easy enough. Simply add a negative "interest rate". At the 
beginning of each election, a certain percentage of the total is removed 
from everybody's credit. Small parties have no chance to accumulate more 
quickly than the interest removes credit from them. To see this clearly, 
consider a -100% interest rate. Then that is the same as having no 
credit at all, which turns the system very majoritarian. On the other 
end, a 0% rate would let every party, however small, win after enough terms.