A note on Democracy

Instead of commenting on the very interesting post by mindframes on Democracy, i just thought it might be better for me to pen my thoughts as a blog.

@ Mindframes: An interesting point that you have brought into focus from your comment to the post on democracy is that if the social planner in a democratic set up is working in favour of the public, then why is it that just a fraction of the population end up voting? Does this represent the the breakdown of the democratic set up or a show of loss of faith in the system from the voters?

I agree that the right to vote is one of the principal determinants of a democracy. But lets look at this problem from a different angle. Generally democracies are big countries with large electorates and a significant number of eligible voters. In theory we can definitely think that the effect of one vote will at best be marginal (but i guess we were proved wrong in the US in the election prior to the last, which we can consider as an anomaly for our purpose here). But lets look at the individual voters decision to vote a little more carefully. Lets say that the net benefit for the individual comprises of two parts. One is the direct cost benefit (let C be the cost and B the benefit, then the net benefit will be N=B-C). The other will be the probability of casting the decisive vote for being on the winning side (just going back to my comment on preferences). THe higher the probability of casting the decisive vote, the more would be my inclination to vote. So let me denote that as (Z=p*X where p is the probability of casting the decisive vote and X represents the benefits derived from being on the winning side).

Now let us compare the two parts of the function individually. While N is straightforward since they are strictly observable, we cannot easily measure the impact on Z, because it has a probability measure p which is affected by the number of people who turn out to vote. To be more specific since voter turnout is endogenously determined and hence not observable prior to the decision to vote. The probability of casting the deciding vote will be near zero if everyone in the electorate votes and vice versa and note that the individual will have no way of verifying if the entire electorate will vote or not. Therefore again assuming rationality and the prior belief that p will be close to zero in large electorates, the decision rule that most individual will apply is that if N<0, then they will refrain from voting. Hence the decision to vote is definitely influenced more by the measurable direct costs and benefits of voting as against pitting themselves against uncertainties.

To take this further, suppose we assume that every individual in the electorate ended up thinking in the same line, then virtually nobody will turn out for the vote and hence every vote could be a decider, which will again make every individual think that his/her vote will be the decider, leading to everybody in the electorate voting. However, I will refrain from this line of thinking for the moment. Another line of thought which might do the rounds is using psychological persuasion modes (sense of civic duty etc etc.). I have chosen to ignore this line of thought (will reserve something on this for a later blog).

Hence for the moment let me use the argument of rational behavior and suggest that the voter turnout is lower not because, voters dont believe in the democratic system or that the social planner is not being efficient, but rather given the circumstances, their net benefit from voting is negative.

@ Survivor: One of the key points raised in your comment is there is no "true democracy". That really did set me thinking and I think my response to that would be democracy really means quasi democracy. While i agree to that and I guess i will reserve my comments on a quasi democracy vs. a democracy to another blog, my concern is with the comment on going to war. "invading other countries", that seems to be a little harsh. While again there might be hidden agendas for the social planner, what seems unclear is how to justify or not justify a single action, especially when there are several interlinking events, which may or may not have caused such a reaction (arguably justifying the actions). The direction of causality cannot be established without doubt and hence i would not go to the extreme to saying that this represents a failure in the democratic set up.

Now to your comment on dictatorship being the best at home as long as you rule! (LoL)..

I think this is an interesting area where we can apply Arrows impossibility theorem. Arrows theorem basically says that there is no ideal voting system in the world. Crudely stated every voting system is flawed. Lets think of the set up where decisions have to be made at home. If we assume that there exists a system for rank ordering of preferences for all the people involved in decision making process and that the preference would be for a collective choice rather than individual choice, how best can we arrive at an optimal choice where one ordered preference function is preferred over all others?

When we talk about collective decisions, we can arrive at a rank ordering of the preferences for each decision in several ways (ie. individuals can have difference preference functions). Let us say we have a choice function (c) which represents the best possible rank ordering of preferences. To achieve the optimal choice function C, there are several constraints that need to be satisfied. One such constraint says that there cannot be one participant whose rank order is most preferred over others (in other words dictatorship is not allowed). For Arrow's theorem to hold there are several other constraints too, but for the sake of parsimony, lets assume that all other constraints hold. Given this scenario, Arrow states that an optimal cchoice function can never be picked.

Hence in this set up since survivor ends up being the dictator, it should be a lot easier to make collective decisions as Arrows impossibility theorem holds.