If politicians were mathematicians
May 12, 2010 6:00 PM   Subscribe

If politicians were mathematicians. "I would like to suggest two systems for parliamentary votes, one that would weaken the party system but without killing it off entirely, and one that would protect large minorities. Neither has the slightest chance of being adopted, because they are both too complicated to be taken seriously. But mathematicians wouldn’t find them complicated at all — hence the title of this post." Fields medalist Tim Gowers messes around with political axioms.
posted by escabeche (18 comments total) 4 users marked this as a favorite
One thing that he doesn't seem to consider as relevant is a written constitution that overrides parliamentary votes.

The second problem is one that is particularly serious in a country that has a large minority with very different interests from the majority ... party representing group B will have a large majority in government, which will allow it to advance the interests of group B at the expense of group A. For example, it could give all the powerful jobs to people from group B, pay for good infrastructure in regions where people in group B tend to live, and so on. This situation is sometimes referred to as the tyranny of the majority.

Instead of proposing any number of odd solutions, it seems easier to prohibit that type of favoritism and declare that the government cannot do that.

On the other hand, if mathematicians were politicians, the act of voting would just be declared a solved problem and they'd move on to something more interesting.
posted by Lemurrhea at 6:12 PM on May 12, 2010 [1 favorite]

Neat. Terence Tao, another Fields Medalist, shows up in the comments.

By the way, speaking of mathematicians in politics, the entertaining Antanas Mockus stands a pretty good chance of being the next president of Colombia.
posted by 7-7 at 6:16 PM on May 12, 2010 [3 favorites]

(Mockus, previously on Metafilter. He has now joined forces with Fajardo, the other mathematician in the race.)
posted by escabeche at 6:19 PM on May 12, 2010

It is this last part that almost no politician would understand, since non-mathematicians have a strong aversion to the probabilistic method.

I don't think the reason that the political party apparatuses which have the power to effect this kind of change are not going to adopt your proposal to strip political party apparatuses of most of their power is their strong aversion to the probabilistic method.

Any idiot can come up with interesting and arguably better decision-making mechanisms than our governments employ today; the trick is to get them passed under the present ones.

And, also, why the idealization of consensus? Has this guy seen the United States Senate lately?
posted by enn at 6:28 PM on May 12, 2010 [2 favorites]

Thank goodness countries aren't run by mathematicians. For one thing, they don't seem to realize that voting is not math. It's a way of having (or specifically a way of ending) an argument without resorting to physical violence. The point is to have the argument, the vote is just a closure ritual.
posted by rusty at 6:33 PM on May 12, 2010 [4 favorites]

It's not that they're too complicated, it's that they're solving the wrong problem, if indeed it's a problem at all.

Majoritarianism's not a function of representation through the electoral system, and changing voting systems will not alter the basic requirement that a Parliament come to decisions based on 50%+1. Any system imaginable can and will be made to work to a majority; it's basic political organising. The proposed system of cards and bids and auctions on votes, for instance, doesn't change the principle that the majority gets its way, it just makes it really hard to get one.

The problem with Gowers' proposals is that he's making the assumption that "consensus" politics is an objectively good and desirable thing, and that Party discipline is inherently harmful. Political scientists, start your dissentions.

And another thing, Lemurrhea, that he's not considering as a check on a Parliamentary majority is an elected upper house. Those wacky British.
posted by Fiasco da Gama at 6:51 PM on May 12, 2010

The founding fathers of the United States devised alternate algorithmic systems in order to deal with discrepancies within the Electoral College. As voting districts in the fledgling country grew, arguments over the assignment of delegates' seats led to the proposal of rationing tables.

But this intermingling of statehood and mathematics was preceded by the Imperial Roman Census, which calculated the valuation of individual assets; the word "census" being derived from the verb censere, to estimate.
posted by Smart Dalek at 6:58 PM on May 12, 2010


Absolutely. Elections aren't about winners. They're about losers -- people agreeing on who lost, and saving their energy to fight for another day.
posted by effugas at 7:00 PM on May 12, 2010 [1 favorite]

What about a more mundane concern: the known problems surrounding voting machines (note that that the very state mentioned in that link, KY, recently had a major voting fraud scandal involving voting machines, and leading to convictions, as covered in MeFi two months back)?

Given continued concerns among voting rights advocates both here in the U.S. and around the world (see for instance the current election in the Phillipines and a recent study about voting machines from India), why not require statisticians to audit elections?

That way, at least if irregularities are caught through random samplings, the problem of easily hacked voting machines (a problem still unresolved) might lead to actual genuine voting reform legislation (that works, not the HAVA stuff that does not).
posted by HP LaserJet P10006 at 7:10 PM on May 12, 2010 [1 favorite]

The problem is that elections do not typically discover a sound majority decision. Little else matters because rule of laws universally apply equally to everyone and majority decision is key to these concepts. The spoiler effect blatantly discards the majority will, and ranked votes can be gamed, for example.

One scenario where voting is more sound is an "option" vote that allows undecided voters to fork their choices between their personal favorite, and the obvious favorite to win their side. This poll has reliable information. It is better than going to an approval voting system because voting for three or more candidates is not decisively winnowing down the field to one's major candidate, or one's acceptable major option.
posted by Brian B. at 8:15 PM on May 12, 2010

Part of the problem with most electoral systems, I think, is on the focus on local representation. This is less of a problem, I think, in the US, where local politicians do tend to have the ability to work for the local constituents in their division (although, of course, they also have the tendency to work for lobbyists instead). In Westminster-style systems, as in the UK, Australia, Canada etc., the influence of strong party discipline waters down the validity of local representation. I have mixed feelings about the way politics in the US works. Lack of party discipline is a nice idea, but it also results in the complete pile of bullshit that resulted over health care.

My local MP has relatively little power to do things for the small local area that elected her. She can raise her voice in caucus, and she can send out newsletters boasting about the funding schools here got (that schools right across the country got), but if she dares vote against her party she'll at least lose preselection, or potentially simply be kicked out of her party.

So why bother so much with small, local electorates? Large multi-member electorates seem so sensible. The UK is ripe for this. How many seats in parliament? 450-odd? Why do you need to divide a place as small as the UK into that many local divisions? Do MPs really have the ability or inclination to work for their local area within the present system? Not at all.

Here in Tasmania we have a rather weird electoral system - there are 5 electoral divisions, and each division has 5 members, which means we have proportional representation. There used to be 7 members per electorate, but the major parties reduced that to 5 a while back to try and kill off the Green party. This failed, as Green support increased, and now the ruling party finds itself without enough members in parliament to choose ministers from, so they're considering increasing it to 7 again, giving a total lower house size of 35 members.

Anyway, in our recent election, we had 10 Labor, 10 Liberal, and 5 Green members elected. Each electorate ended up with 2 Labor, 2 Liberal, and 1 Green member. A beautiful example of proportional representation, reflecting as close as possible the actual way people voted. The result is complicated, and there was a month of wrangling and deal-making that happened before the government was decided, but I am extremely happy with this. No, consensus isn't always a viable way to get decisions made, but neither is absolute perfect majority.

My idealistic theory? I want to start the Democratic Proxy Party. Members of this party hold no common policy, except to support reforms that enhance the democracy of the system. Members are required to go to the electorate on issues - mailouts, polls, to gauge how the people who elected them feel on issues. Their worth as a politician will be determined on how well they represented the consensus view of the people who elected them, rather than on how well they held onto a specific ideological position. The Tasmanian system allows this, by the way, because when you get to vote, you are faced with multiple candidates from the same party, so you can focus on the individual rather than the party if you wish. Yes, it would be hell, and there's the potential for the politically active members of the population to dominate policy, but I guess you can't complain about policy if you choose to ignore it.
posted by Jimbob at 8:19 PM on May 12, 2010 [1 favorite]

just wonder how much difference it would make if politicians understood enough mathematics to be able to understand an argument of more than one sentence.

This makes about as much sense as the sentence "What if politicians understood enough English to be able to understand a system of equations with more than one unknown?"
posted by ROU_Xenophobe at 8:36 PM on May 12, 2010 [1 favorite]

the act of voting would just be declared a solved problem

It's worth pointing out that the Arrow theorem isn't about voting, it's about any system for aggregating individual preferences into a collectively binding decision (or preference ordering).
posted by ROU_Xenophobe at 8:41 PM on May 12, 2010

That way, at least if irregularities are caught through random samplings, the problem of easily hacked voting machines (a problem still unresolved) might lead to actual genuine voting reform legislation

I had a thought during the last scandal that we should reinstate charging one dollar per voter. Then there would be another paper trail, with a receipt, and all those accountants, and we could possibly sue for fraud if there was a tally discrepancy.
posted by Brian B. at 8:45 PM on May 12, 2010 [1 favorite]

Interestingly/coincidently, there is an article in the Irish Times today about how former Irish president Éamon de Valera almost ended his life in politics before it began in favour of mathematics when he narrowly lost a bid for a post of professor of mathematics in University College Cork in 1913.

The article goes on to explain that there is some evidence that he applied mathematical concepts to political issues, including set theory when sketching out diagrams of the relationship between Ireland and the Commonwealth.
posted by unbearablylight at 3:32 AM on May 13, 2010

The method of probabilistically changing votes is used in psychological research to investigate taboo topics. You put a person in a room alone, with some questions about taboo subjects: say, something like, "Do you have homosexual desires?" with instructions to flip a coin before answering. If the coin comes up tails, answer honestly. If the coin comes up heads, answer "Yes." That way, if they answer "Yes," no one except them knows whether they answered "yes" because the coin turned heads or not.

You can still estimate the number of people who would have answered "yes"without the coin trick by simple algebra.
posted by Philosopher Dirtbike at 5:40 AM on May 13, 2010

I posted the following comment there :

I’d agree that reducing representative accountability to party whips and campaign donors sounds like a noble goal. We’d surely however lose exactly the same degree of accountability to voters, which dose not sound wise. I suspect the powerful would learn how to manipulate your system better than our current system.

Deliberative democracy however provides another solution :

All representatives vote not just yes/no/abstain for a bill, but also name an advocate for their position. A bill no longer becomes law once passed, but must instead then pass a jury trial, and all advocates supported by enough representatives, say 5%, may argue for acceptance, rejection, or modification. If the country has a president, his veto would be eliminated, and instead he’d appoint and advocate too.

Jurors are selected purely randomly from the voting population, and advocates may not challenge jurors, but instead juries are quite large, say 100–200 people. Jurors’ votes are naturally anonymous, making them accountable only to their own conscience.

I believe this system would provide exactly the benefits you seek from anonymity while keeping the representatives themselves fully accountable. In particular, we’d see multiple advocates from all the major parties, proposing slightly different modifications. Yes, the party whips could limit diversification, but sending too few advocates would often prove suicidal.

In addition, we expect this deliberative trial phase would be extremely good at :

(1) cutting pork barrel spending : Even if your collation partner sends an advocate that supports your health care bill overall, they’ll likely backstab you by advising the jury to cut that new power plant you snuck in.

(2) giving minorities a voice : If you read the experiments comparing opinion polls with `deliberative opinion polls’, you’ll find an overall 10–20% movement towards the position independent and knowledgeable people more often hold, like being pro-choice or less racist.
posted by jeffburdges at 8:47 AM on May 13, 2010

Yes, that works very well when your considering individuals that cannot game the system Philosopher Dirtbike, but companies and politicians would find tricks for using the vote swaps to consolidate power.
posted by jeffburdges at 8:59 AM on May 13, 2010

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