[EM] Challenge: two-party methods

[Juho Laatu]

First I'll try to clarify the definitions a bit. It is so obvious what a two-party system is, but when I think more carefully it is not that clear.

Two-party system:
- has a single-party government
- one of the two major parties forms the government and the other one forms (the main part of) the opposition
- the two major parties alternate in government and opposition roles
- has typically one or more representative bodies
- government may be elected directly (e.g. the president of the U.S.) or based on the power balance of a representative body
- government has typically or often majority support in the representative bodies (this means that third parties are usually small enough not to disturb the bipolar balance)
- members of the representative bodies come typically but not necessarily from small districts with few representatives, often elected using single-winner methods


On 10.7.2011, at 12.03, Kristofer Munsterhjelm wrote:

> 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.

One problem here is that we are slipping away from a two-party dominance towards a system where the ruling party is dependent on the support of smaller parties. That gets close to a coalition government although I understood that the government would consist of representatives of one party only. The government probably does not have majority in the representative body, so other parties may stop progress and cancel their support to the government at any time.

I was also worried that the right wing will not get 50% of the seats although they got 50% of the votes because of the method that favours large parties. The small party may thus spoil the election also this way.

> 
>>> 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 :-)

Is it then so that the largest coalition will get 50%+1 seats? Maybe the largest coalition based on given votes, not based on the seats that they would win without this rule (to cancel the balance shifting effect of the method that favours large parties) (?).

> 
> 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.

That is one approach. That sounds pretty much like an exactly proportional method. Usually two-party countries don't have good proportionally in the representative bodies (except maybe between the two major parties). In the USA the representative bodies are clearly dominated by two parties (in the UK less so). Also my example method would allow third parties to get seats in the representative bodies (after they grow in size). That new balance in the representative bodies would not change the fact that in the USA the president (that is elected using a single-winner method) forms the government. The government could easily lose majority support in the representative bodies in my example method although one of the two major parties would always for the government (without requiring coalitions or support from minor parties). One could complement that method by making it easier for the government to rule even if they don't have majority in the representative bodies (assuming that we want to allow third party representatives in the representative bodies already before they become "second parties"). As an alternative to the 50%+1 approach one could require some appropriate supermajority to stop government proposals.

The obvious alternative to electing also third party representatives in the representative bodies would be to elect their candidates only after they reach "second party" status nation wide.

> 
>>> 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.

Is it enough if the voters give sincere rankings and the C supporters can see that in every election party C gets closer to replacing party B as one of the two major parties?

> 
> 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.

Yes, that is maybe the main difference to current plurality based elections. The intention is that the example method would have also less spoiler problems than IRV has.

> 
> 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 already mentioned the ease of giving sincere ratings and the visible increasing support in the election results. I mentioned also two options, either to allow or not allow third parties to get seats in the representative bodies (from the single-seat districts). In the former case voters would see also concrete representatives before they get the major party status. One could btw also make some intermediate arrangements so that the major parties will get most of the seats but third parties will be given some "observer seats" (for example 90% to the two major parties (proportionally) and 10% to the minor parties (proportionally)). I note that some seats in the representative bodies may be e.g. representatives of different states of a federation,in which case they are maybe elected locally without considering which parties are major parties at national level.

> 
>>> 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.

But if that coalition changes from one election to the next, then I think many multi-party countries operate that way. Governments agree on a program that then ties the opinions of all the parties for the whole election period. In that sense they form a new party with new (compromise) policy for the election period. In some countries like Sweden left and right wing have to some extent grown into coalitions that may alternate in power. If the coalitions are as stable as in Sweden, then we start getting some two-party flavour in the system. But maybe that system is still more on the multi-party side since all parties still have their own programs and a new government policy has to be negotiated every time due to changes in the support level of the coalition members.

Also the coalitions may break if the parties of one wing gain clearly more or less than 50% support. Or if those two stable coalitions will not break but voters will instead establish the 50% - 50% balance again between these coalitions after the complete coalitions change their policy (more in line with the other coalition) as a result of losing votes (as in proper two-party systems), then we are maybe getting again closer to a de facto two-party system.

> 
> 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.)

I note that for example in Finland there have been three large parties, and all coalition combinations of there three (complemented with some smaller parties) have been possible. Now there are four large parties and the politicians are a bit confused :-). The coalitions are thus not stable from one election to the next. The multiple parties can be categorized in multiple ways. In addition to the traditional (but nowadays not any more that dominating) left - right axis there are also other divisions like city vs. smaller places, greenish vs. not, global integration vs. not, liberal values vs. conservative.

If politicians can behave well despite of having different opinions, and they can find joint programs when they form majority governments, then II'm happy with having lots of small opinion groups and having proportional representation of even the smallest minorities. But of course now I'm deviating from the ideal of two-party systems, that should rather be to rely on the two major parties to find the median opinion of the voters efficiently.

> 
>> (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.

I believe also most STV systems use parties to form the basic structure of the political field. The STV method allows voters to ignore the dividing lines between parties but probably most voters still think mostly in terms of parties anyway. They may be happy to make some exceptions in the pure party based ranking though. So, in politics simplified party  based thinking is a good approximation of political environments anyway. (Associations where there are no parties and people maybe do not want to have parties things are quite different. But that's a different story.)

> 
>>> 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.

I easily tend to think the same way, but maybe that is because I was born in a multi-party country. But one can see that two-party democracies are not doing too bad either. Many of the leading nations have that system. And in order to make this challenge fly one must have an idealized model of the two-party approach (roughly "to find the median opinion between the two major parties").

> 
> 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.

Yes, those two parties often seem to be on the other side of the dividing line in the hope of getting some additional votes that way. And after the election things may change, and the policy returns back to some more extreme track. But on the other hand multi-party systems are also not immune to these problems. Centrist opinions are often popular during the election campaigns (although some parties find their niche elsewhere too). And it may happen that the policies of governments often build on making decision that those parties that are in opposition would not make. I.e. also multi-party majority governments may swing the system in one direction while in power.

But I guess multi-party governments are typically a bit more compromise seeking. In two-party systems one fear is that there are smaller questions that never become the key questions of some elections, and therefore changes might never take place although majority of the voters might want such changes. Two-party systems may thus be less flexible because of their simplified structure that in a way assumes only one one-dimensional opinion spectrum where the median opinion moves.

> 
>> 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.

My basic assumption was that parties would not actively use the ballots in their account but the winner of the election would automatically lose some appropriate part of its ballots. But anyway, the winning party would eliminate also some ballots of a losing party. Can you give a more detailed example. If one party decides to give additional votes to another party, and then later takes these away, then no harm has been done. If that other party wins an election before the first party then those approval ballots helped that other party eliminate some such votes from the first party that would otherwise have been safe (=no risk of elimination).

I did no consider teaming but assumed that all parties run alone. If we allow some coalition to win the election (maybe form a government after negotiations) then we should elect votes from the whole coalition in some appropriate way.

> 
>> 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.

Yes. Negative interest rates may however have also some problems. If we are in a situation where party A has 130 credit votes (all bullet votes) and B has 70 credit votes, then A wins, and we will erase 100 of its votes (=> 30 credits left). In the next election both will get 50 new votes. Now A has 80 credit votes and B has 120. B wins and loses 100 votes (=> 20 credits left). In the next round we are back in the starting position (after 50 votes to both) (if there is no negative interest). The problem is that A is all the time higher in the credits. It will thus lose more votes to the negative interest. The system brings the credits of the two parties closer to each others. And as a result the alternation of the two parties becomes more regular "one term in government, one term in opposition". That is probably not the target. That in a way cancels democracy. In a two-party system a party that voters like should probably get more time in government in some proportion to the number of votes it gets. Note that the difference in support between the two parties may be rather small. (This kind of credit based system may actually alternate too regularly anyway when compared to current systems, and it may therefore need some fixes to give more weight to the typical small changes in popularity.)

Juho