Westlake’s impossibility theorem

Kenneth Arrow

Kenneth Arrow

When I was studying for my Master’s at Johns Hopkins University I had to write a paper on Kenneth Arrow’s impossibility theorem (otherwise known as ‘Arrow’s paradox’ – in the fashion of ‘Xeno’s paradox’, I suppose). Arrow, who was joint winner of the Nobel Memorial Prize for Economics in 1972 at the age of just 51, demonstrated the theorem already in his PhD thesis but went on to give it a broader audience through his Social Choice and Individual Values (1951). In a very elegant nutshell, Arrow demonstrated that democracy is impossible (you can read about his theory here). At Tim Smit’s talk (see 10 February post) I asked a question which I am (half-seriously) thinking of firming up into ‘Westlake’s impossibility theorem’. The theorem goes as follows: a) democracies are predicated on political parties seeking to gain power by aggregating a sufficient number of votes so as to win a majority; b) political parties are rational entities, which means that they will always act to maximise votes (or to minimise vote loss) for the next electoral challenge they face; c) policy choices to enhance sustainability necessarily involve benefits that will not be achieved within a single electoral cycle and costs that will be incurred within a single electoral cycle; therefore, democracy and sustainability are mutually incompatible. I rest my case. Help me out of this depressing predicament, please.


  1. Steve

    Even assuming all your premises are valid, which is arguable, you’re finally assuming that the electorate is incapable of recognising a short term cost for a long term gain without punishing the government. A sad view of the world, but one, I think, which is not valid.

    Even if the incumbant leaders were to be replaced I don’t see how this is the end of democracy, surely they’ll be replaced – via an election – by another democratic party who may, or who may not, reverse earlier decisions.

  2. Julien Frisch

    The assumption that political parties are rational entities is not necessarily correct, because the rational behaviour of individual party members does not necessarily lead to rational behaviour of the collective entity (I think rational choice theory has shown this in extensio).

    One example: An individual that wants to stay in power might well propose long-term policies to legitimise her/his long-term ambitions. If others catch up with this orientation (to steal his/her competitive advantage), the spill over from individual rational behaviour could lead to a long term orientation of the group.

    And I haven’t mentioned theories of socialisation yet.

  3. Martin

    OK, Julien, there are indeed cases of individuals within parties enhancing their own medium- to longer-term chances at the cost of their parties’ short-term chances, but as a general observation parties, as entities, try to stay in power. In my days as a political scientist I only found one true counter-example. It was a candidate in a by-election in the UK back in the 1950s. He stood on a platform of ‘don’t vote for me’ but actually won 10 votes. Could this be the least successful candidate ever?

  4. Julien Frisch

    What I wanted to say is rather that by presenting long-term political goals, a candidate might have higher chances within the party to become elected (“I will make this country the most competitive in the region over the next 10 years…”; “I will foster renewable energies [which needs more than one election period]”) because this looks more like a positive vision for party members than just an orientation towards the next elections.

    If others within this party rationally adapt to this strategy, those long-term (or at least longer-term) orientations could become a general policy of the party.

    And if such a policy orientation remains alive, the party and its leadership will be able to shape the public and internal discourse in a way that make this approach more electable, thus making short-term orientation a less desirable behaviour.

    In the end, the short term orientation of being re-elected could only go together with a long-term policy orientation – and the rising dominance of climate protection discourses across party boundaries shows that in certain policy areas this is possible.

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