The Curious Case of Senate Filibuster

American Constitution states as clearly as it ever states anything, that to pass a law majorities of House and Senate are required, and doesn't know anything about filibuster process - this silly Senate regulation in which 60 votes are required to even bring anything to final voting.

And it would be so easy to get rid of such rule - mere 50+VP majority in Senate can change Senate procedures. Even more curiously - it would clearly be in interest of the majority party - be them Republicans or Democrats - to get rid of such silly rule. The argument that they might want to keep it for the future, as they might end up in minority later is obviously wrong, as your Democratic/Republican Senate keeping filibuster doesn't do anything to stop the next Republican/Democratic Senate from abolishing it.

Persistence of such major non-Constitutional feature which clearly favors the minority party is extremely curious.

Voting Power

The mystery will be resolved soon. For now let's step aside for a moment and imagine a Parliament of a fictional European country with four parties - Armadillo Party, Bear Party, Cat Party, and Dog Party, with 45%, 45%, 6%, and 4% representation in their Parliament. As it's a fictional country, let's assume perfect party discipline, and simple majority required to pass anything. How important are the parties?

Naively looking at their statistics, it would seem that Armadillo and Bear parties should be vastly more important than Cat Party, which should be just slightly more important than the Dog Party. This is entirely wrong. To pass anything you need one of the following sets on board:

• Armadillo Party and Bear Party
• Armadillo Party and Cat Party
• Bear Party and Cat Party
  

The Cat Party with its 6% of vote has as much power as Armadillo and Bear parties with 45% each! And Dog Party with its 4% has no power whatsoever - its support makes no difference for whether a bill will pass or not!

This highly counterintuitive result is mathematized as two "power indexes" - Banzhaf power index and Shapley-Shubik power index. They differ in minor details, but basically they tell you how important are different players in a complex voting system.

Now there's important caveat with voting power indexes - they assume interests of parties are entirely independent - Armadillo Party is as likely to agree with Bear Party as with Cat Party as with Dog Party - something which is not true in the real world at all. No see why it is important imagine a Bear-Cat coalition - having 51% of votes together they have 100% of power, while Armadillo and Dog Parties become entirely irrelevant. Why wouldn't Bear and Cat Parties want to start one? Mostly because coalition victories won't do you any good if you don't agree with other coalition members. Bears might push for taxpayer subsidies for honey production, something that Cats would much rather not have - and could shut down the idea together with Armadillos if they weren't in this silly Bear-Cat coalition. Increased coalition's voting power is usually countered by having to vote for things coalition wants that you're not terribly enthusiastic about.

Anyway, let's look at American system, both as its specified in the Constitution, and as it works with the filibuster. USA is no Europe, so we cannot assume any Party discipline - let's go further and assume every Representative's and every Senator's votes are entirely uncorrelated. This isn't true for many issues which follow left-right party lines, but is very much so for the highly essential pork barrel spending and other things they do for lobbyists in exchange for campaign contributions. The only exception to the independence rule I'm going to make is assuming that Vice-President always does what the President tells him to, and is no independent actor. If there were any votes in history in which they disagreed, I'd like to know about it.

Assuming I coded it right, Shapley-Shubik voting powers of the President, individual Senators, and individual Representatives in Constitutional system are 16.66%, 0.391%, and 0.102% respectively - president is worth almost 43 Senators, and a Senator is worth 3.8 Representatives. By the way that's why elections for President - supposedly "executive" function - focus primarily much on legislative issues. American President has large levels of control over legislative and judiciary branches of government, in addition to his executive responsibilities - as extremely unhealthy concentration of power.

Now with filibuster, the situation changes drastically - President's power drops to 9.115%, Senators' powers increase to 0.716%, and Representatives' plummet all the way to 0.044%. Now President is worth only 12.7 Senators as opposed to previous 43 - and more what's even important - each Senator is worth over 16 Representatives!

Numbers are considerably different with Banzhaf index - it's 3.996%, 0.295%, 0.153% Constitutionally and 2.468%, 0.564%, 0.094% with filibuster - but the story is the same - filibuster greatly increases Senator's powers. Knowing that it's not terribly surprising that Senators are not too eager to abolish filibuster - they would be giving away a lot of influence with it!

This result might be surprising at first, but there's straightforward intuition behind it - if there are multiple requirements for a law to pass - the one which is most difficult determines the process - Constitutionally passage in House and in Senate are equally difficult, giving each of them equal powers - but if Senate decides to make passage harder - it will be very unlikely for any bill to have 60% support in Senate without also accidentally having at least 50% in the House.

State Size

But wait - there is more! Small states are massively over-represented in Senate, while having only fair representation is House of Representatives. By unduly strengthening the Senate, filibuster increases power of small states. By how much? As situation becomes a bit too difficult for exact methods, I ran a quick Monte-Carlo simulation of Shapley-Shubik voting powers, assuming all states vote as blocks - so we have 50 states voting, each with 2 Senate votes and some number of House votes; plus independent President.

Constitutionally President has 14.88% power in such case, the most populous state California 8.08%, while the least populous states with one Representative like Wyoming has 0.79%. That's a huge unfair and undemocratic overrepresentation already - California has 69x the population of Wyoming, but merely 10x as much power. With filibuster it gets far far worse - President's power drops to 9.49% - not surprisingly since more of it goes to Senate, but now the difference between California and Wyoming is merely 5.10% to 1.34% - 3.8x. Californians are underrepresented relative to Wyomingites by a factor of 18x. Not terribly democratic, is it? Actually I'd love to discuss the point that less democratic systems like American are not in any obvious way less effective at solving real world problems than more democratic systems like let's say German - but let's leave that for another post.

Even if you're from a small state, you shouldn't be getting too happy - small state Senators are the most corrupt members of Congress, and the baseline isn't terribly good either. There's the usual disclaimer that power indexes refer to idealized situation in which everyone votes independently from everyone else - which describes pork barrel spending and miscellaneous lobbying much better than it describes issues of economy or abortion. Still, let's not be as naive as Al Gore about the Senate - if this lobbyist-infested place couldn't even get popular, life-saving, deficit-reduring, and sensible from every other possible point of view public option, what are the chances of it passing expensive and unpopular climate bill which will only benefit some Bangladeshis decades from now? Nobel Prize offers no protection from wishful thinking.