Health Care

Health Care: Beyond Prisoner’s Dilemma

By Karen Tumulty | March 5, 2010 | +

Okay, geeks, this one’s for you.

I hereby concede that I am out of my depth with regard to the complex processes that could determine the outcome of the upcoming health care vote. Particularly when it comes to my grad-school understanding of game theory.

At his blog IPBiz, Lawrence B. Ebert looks at my Prisoner’s Dilemma post from yesterday and makes the argument that another, potentially more relevant exercise to look at is Nash’s Equilibrium:

IPBiz notes that long before game theory and the prisoner’s dilemma, strategic voting existed. In the case of the vote of Edmund Ross in the impeachment trial of Andrew Johnson in 1868: But Ross’ vote wasn’t the lone act of bravery it was later made out to be. At least four other senators were prepared to oppose conviction had their votes been needed–a fact that has been forgotten [from Slate] More recently, strategic voting has been discussed in the healthcare saga: One lone House Republican voting for the reviled Democrat healthcare bill.

Of Nash equilibria: The Nash equilibrium concept is used to analyze the outcome of the strategic interaction of several decision makers. In other words, it is a way of predicting what will happen if several people or several institutions are making decisions at the same time, and if the decision of each one depends on the decisions of the others. The simple insight underlying John Nash’s idea is that we cannot predict the result of the choices of multiple decision makers if we analyze those decisions in isolation. Instead, we must ask what each player would do, taking into account the decision-making of the others. (…) The contribution of John Forbes Nash in his 1951 article Non-Cooperative Games was to define a mixed strategy Nash Equilibrium for any game with a finite set of actions and prove that at least one (mixed strategy) Nash Equilibrium must exist.(…) Of the prisoner’s dilemma, the globally optimal strategy is unstable; it is not an equilibrium.[from wikipedia]

And from the incomparable Swampland comments section come two other arguments:

From commenter mfbattle:

This is not the Prisoner’s Dilemma (because I should also tell the police in a one shot game, but play tit-for-tat in an infinite repeated game (see Axelrod’s tournament) ), but rather it is best explained by the Lighthouse story. Imagine a fishing community by a rocky shore. They all want to build a lighthouse to keep the boats safe. The lighthouse will cost $15, and there are 25 fishermen. So if each pays $1 they get the lighthouse. Now, if I pay the money and the lighthouse is not built I lose a dollar (imagine a nasty builder). If I pay the dollar and get the lighthouse I benefit from the lighthouse but I still have lost a dollar. If I don’t pay the dollar, but 15 others do, I also get to benefit from the lighthouse. Should I pay the dollar? Well only if 14, and only 14 others, pay a dollar. Otherwise I waste a dollar, either by paying and not getting the lighthouse, or by paying and the community collect more that $15. The real problem is that if I don’t know what the others are doing should I gamble and pay the money. I have played this game in about 10 classes, and the lighthouse has NEVER been built.

Commenter rimmyrimrim comes at this from pretty much the same direction, citing a game theory exercise called Volunteer’s dilemma.

Of course, this is not a game we are talking about here; it is a big decision that will affect the lives of millions and millions of people. Nonetheless, it is sort of interesting and thought-provoking to take it, at least for a moment, out of the partisan realm, and into the academic one.

Any game theory exercises we are missing?

Related Topics: game theory, lighthouse, nash's equilibrium, prisoner's dilemma, volunteer's dilemma, Congress, Health Care

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  • spob

    It’s a variant of the free-rider problem. A Dem voting “no” gets the benefits of passage, but reduces the downside.
    .
    Keep in mind, this bill is unpopular, and that counts for something.

  • shepherdwong

    “I have played this game in about 10 classes, and the lighthouse has NEVER been built.”
    .

    Of course, this is not a game we are talking about here; it is a big decision that will affect the lives of millions and millions of people.

    .
    I’d be willing to bet that in mfbattle’s 10 classes, there was no burning desire for a lighthouse.

  • destor23

    Should we really use phrases like “strategic voting” to describe this? In the end, I want to know what my federal reps believe. It’s the only way I know whether or not I should vote for them. “Strategic voting” is simple dishonesty. “I want the President impeached but I don’t want to do it” is not a position. It’s cowardice.

    It’s dangerous to democracy because it robs people of their right to judge their representatives by their beliefs and actions.

    But to your question, any game theory exercises we’re missing here? How about shaming? Because the perverse part of this is that the liar who engages in a “strategic vote” often comes off looking principled and brave.

    We’re just not calling these people out for their follies.

  • http://patricksartor.wordpress.com patricksartor

    The “free rider” I am familiar with when it comes to unions.
    If there are ten grocery stores (or chains) and seven of them unionize, in order to get the same workers and not face the hardship of a wildcat strike, the other three will pay the same benefits to non-union employees without the union.
    So, since trying to start a union can (not in theory, but in reality and in this theory) get you fired and requires a huge amount of work, nobody wants to the first organizer of the first grocery store but always to wait for everybody else to do the work.
    It is, also, with the union organizing this is true. You can sit there and do nothing and the organizers take all of the risks and, at the end, you all get the same benefits.
    However, if nobody does anything, you will all be struggling at a low wage.

    In this case, if the bill ever gets past and Republican obstructionism and propaganda stop when theirs is a lost cause, the bill will, retroactively, become popular.

    (History is full of these things including Harry Truman and Abraham Lincoln among others not popular at all in their own time but got more so over time.)

  • the committee

    Do I love the KT? Oh yes I love the KT.
    .
    There needs to be irrationality thrown into the system, I think. In the Lighthouse case: not only are players calculating the likelihood that others will throw their own dollar in; should a player throw in, she also has to anticipate being compared to Hitler in the near-term, and seen as inept if the lighthouse turns out to be a leaning tower in the long term. She also has to worry about throwing in a dollar only to have another player, plus a few more to be named later, sink the whole project because they are concerned with fetuses.
    .
    Then there is the consideration that if the lighthouse doesn’t get built, the community–well, besides the people who could have built three or more lighthouses on their own dime–will go broke and starve. On the other hand, there are a number of scenarios looming in which everyone goes broke and starves anyway, so maybe it’s better for our player to reap the short term benefits of not building the lighthouse, and hope that she’s fit enough to survive coming catastrophes in the long term.
    .
    Ah well. Here’s hoping healthcare passes and that it’s adequate to ward off mass bankruptcy. Then let’s get on to the other crises threatening national ruin.

  • square1

    You can also change “lighthouse” to “climate change solutions” and multiply the number of people by 500 million.

    BTW, the lighthouse still doesn’t get built.

  • deconstructiva

    KT, sorry to be late to the prom but maybe HCR is like one of Zeno’s paradoxes, esp. the dichotomy one where as you approach the finish line you cut the distance in half, then you cut the remaining distance in half, then cut the next dist. in half, etc. etc. etc. etc., meaning you never reach the finish line.

  • deconstructiva

    KT, maybe HCR is also like another Zeno paradox: the arrow. Like an arrow in flight, HCR is in motion towards its goal of universal coverage. However, that arrow at any given moment travels no distance during that moment – just like at any given moment of HCR negotiations there is no movement and everything just stalls. Therefore, nothing moves at any instant, but since time is entirely a string of instants, nothing moves at all. HCR remains stuck forever. Does this help you out too?

  • keillrandor

    Strangely enough, this is related to a paper I’m working on – the term ‘game’ in the English language, is, (and has been), used in ways which cover both productive, (work), and non-productive, (play), activities. The belief that it HAS to be non-productive, (play), in order to be a game, appears to be a fairly recent phenomenon too.

    One other thing to bear in mind, is that if games were only about play, (non-productive activities), then the English Language actually has no equivalent of a game for work, (productive activities). (And since the difference between work and play is purely subjective anyway, none of it really works that well to begin with in many situations – but that’s another argument for another day :p).

    The main thing my paper is about, is the foundation of understanding what games actually are – (since they’re not fully understood at this time – (which is a symptom of a much larger problem)) – separate from the purely psychological/mathematical methods and mechanics they use.

    Of course, game theory and the prisoner’s dilemma etc. are ALL purely psychological problems and puzzles.

    So, how good are the reporters at Time magazine on the psychology of politics and politicians, because that is the main problem we’re dealing with here…?

  • keillrandor

    (doh – apologies for the lack of paragraph breaks – (I forgot :-/ )).

  • mfbattle

    You are right about my students desire for a lighthouse. Of course if I was as smart as you are, I might tell the students that they all get 5 points of extra credit on an exam if the lighthouse is built, but if they pay the dollar towards it they lose 2 points. This would mean that there are the following options:

    1) Pay the dollar and the lighthouse is built – get 3 points on the exam
    2) Pay the dollar and the lighthouse is not built – lose 2 points on the exam
    3) Don’t pay the dollar and the lighthouse is built – get 5 points on the exam
    4) Don’t pay the dollar and the lighthouse not is built – get 0 points on the exam

    PS. I would offer them the choice of not playing at all (but only 2 or 3 ever don’t play)

  • mudlock

    Strategic voting isn’t necessarily dishonest.

    Consider an election with three candidates. Suppose that one, your personal favorite (+10), is polling at a measly 2%, while the other two, one of whom you absolutely despise (-10) and the other you find just a little distasteful (-1), are both polling around 48%.

    The strategic vote, is to vote for the distasteful candidate. It’s not dishonest, it’s just the one that give you the highest expected utility.

  • http://patricksartor.wordpress.com patricksartor

    One thing I just thought of is that, if this lighthouse of HRC does not go through, who wants to be the sevenths American president to attempt to propose health care reform (Theodore Roosevelt, Republican, Franklin Roosevelt, Democrat, John F. Kennedy, Bill Clinton, Barack Obama).
    If it looses this round, who wants to play this version of lighthouse again?
    Who will take a presidential candidate who makes health care reform a part of his or her platform seriously?

    Imagine this part: if the lighthouse does not get built, you teacher gets fired, too.

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