Saturday, May 19, 2018

The Hanging Rules
There was a time when algorithms were considered more important if they did not depend on the nature of data they processed. Take sort algorithms, for instance. They work just the same whether you sort the weights of a set of pigs, or the age of a set of galaxies. I have no quarrel with such algorithms; in some sense they deal with the highest level of abstractions such as numbers.

However, nowadays the challenges are more in dealing with large volumes of data from different application domains. Knowledge related to the domain are basic to success with most of our endeavours. Computations of this type do not necessarily lead to unique solutions to a given problem. However, the solutions they provide could have great value. This value arises from the importance of problems they help us solve.

Why this build up for what is to follow? It is because I wish to discuss a very important problem. It is the problem of shaping pre-poll alliances among political parties. It is clear that the Indian election to be held in 2019 will critically depend upon pre-poll alliances. The recent Karnataka election has high-lighted the significance of alliances. Commentators have pointed out that had there been a pre-poll alliance, the outcome would have been quite different. Pre-poll tie-ups will be important for all parties: those with a high vote share as well as for the smaller parties. When vote shares are added together, the winner may not get the aithmetic sum of the two vote shares. When two parties with vote shares (expressed as percentages of votes cast) A and B have an alliance, the winner does not get the vote share A + B but may get something like A + B/2. The effect on the election results could however be very dramatic. Pre-poll alliances have demonstrated their effectiveness in the past in this regard. Increasing your vote share by B/2 does not just increase your chances of winning by 50%. It may increase it 500%.  

Given this logic, why do parties hesitate to enter into pre-poll alliances? Partly because reliable predictions of possible gains are not available. Secondly, there are no clear procedures which can be used by the parties concerned to decide on how they should share constituencies between them. How many constituencies would each party get? Which constituencies would be assigned to which partner? These are complex questions, even when only two parties participate in a pre-poll alliance. Multi-party computations are more complex, but the generalization form a 2-party to a multi-party situation is not very difficult.

The major difficulties in persuading political parties to consider this problem analyticaly is that solution should be fair to the potential allies and must be seen to be clearly unbiased. The solution should also be easy to communicate and understand. The solution cannot be thrust upon the parties involved and must leave some room for tweaking as per their intuition and perceptions. I will offer a solution here to the two-party problem and leave it to the reader to generalize it to the multi-party situation. I don’t mean to suggest a solution that should be adopted blindly; I only wish to have many people think out their own versions of the solution. Secondly, I want to keep the solution very simple. You can make it more accurate as a predictor of the gains of a pre-poll alliance by making it more complicated, but very few political leaders are computer scientists. It is difficult to persuade them to adopt what sounds like mumbo-jumbo to them!

Lastly, why the funny name? It comes from the saying “If you don’t hang together, you will hang separately”! So, this is a solution that shows how some politicians could hang together!

The solution: 
  1. Assume that the vote share received in each constituency in the last election is the best estimate of the vote share that a party would get in the forthcoming election.  
  2. If the estimated vote share A of one of the two parties is greater than that of the other B, assign that constituency to the party with the higher estimated vote share.
  3. Compute the total A + B/2 where B is the vote share estimated for the other partner. Let C be the highest vote share estimated for the strongest party outside the alliance. If (A+B/2) > C, mark that constituency as a strong seat for the proposed alliance. The underlying assumption is that an alliance does not transfer all votes of from one partnering party to the other. For simplicity, we assume that 50% of the votes can be "transferred". (carry out the above three steps for each constitutency).
  4. Make adjustments to the extent of 20% of the seats by negotiation, provided this does not disturb the assignment of any strong constituency. However, the number of seats assigned to partners should be in proportion to the total vote shares each has earned.
  5. The above rules are not written in stone. But if the two partners cannot agree to some reasonable modified version of the same, they can hang separately!

          Srinivasan Ramani       

No comments: