Interdependent Utility Functions, Johnson, and Scotland's referendum

Last Thursday's referendum in Scotland to decide whether the nation would break its 300 year old tie with the United Kingdom broke the record for the highest voter turnout in a U.K. election history, with 84.5% of registered voters casting ballots on the decision.  The new record-- beating out the general election turnout in 1950-- got me thinking about the Rational Abstention piece of Johnson's argument presented in "Voting, Rational Abstention, and Rational Ignorance".

 At its most basic, the Rational Abstention argument states that it is rational for citizens not to vote in an election because the expected  benefit for doing so will be smaller than the  cost of voting.  Johnson's argument is that expected benefit for a specific voter is equal to the probability that that voter's vote decides the election multiplied by the difference in the voter's utility between election outcomes.  The expected benefit of voting is often so low because of the large quantity of voters in a given election; even an individual that highly values one election result over the other will not have a high expected marginal utility if there is a large number of voters to reduce the probability that his / her vote will have an impact on the election.

The 84.5% turnout in Scotland's recent election in light of Johnson's theory is interesting.  With over 3.6 million total votes, the probability that an individual's vote would decide an election is 0.00000028.  An individual who values either leaving the U.K. or staying in the U.K. over the option by $1,000,000 would expect the benefit of voting to be around 28 cents.  Even those who value the election at 10 million dollars would only expect to receive a benefit of $2.80-- almost certainly higher than the cost of voting.  So why such a high turnout?

I have 2 ideas that work within Johnson's theory.  The first is one we discussed in class: individuals receive utility from voting that is not affected by the number of voters.  Utility from guilt aversion, feelings of civic duty, etc will be gleaned by the voter regardless of the probability that voter's vote actually matters in the election's outcome.  The Scottish referendum was a highly covered, globally important election, and the normal utility categories unaffected by the election outcome will be amplified.  The other idea has to do with our discussion of interdependent utility functions.  Because the decision to leave the United Kingdom would have enormous long-term historical, economic and political effects for Scotland, it is not unreasonable to expect that strong national pride could create interdependent utility between voters and their country.  In this case, voters would value one election result over the other not just in terms of personal gain, but the potential gain or loss to be had by fellow countrymen and the reputation of their country itself.  Many voters, then, could be expected to value one election result over the other at values that would make B greater than the cost of voting.  These dollar values would have to be quite large, and I could not see this happening in a normal vote for an elected official, but I do not think this is unreasonable in elections with enormously significant consequences like Scotland's recent election.