Proportional representation

The AAP manifesto mentioned something about “supplementing the existing first-past-the-post system with proportional representation.” This was a pleasant surprise — it mirrored something I’d discussed with friends in 2010.

In response to a bunch of constraints that people threw up, I had proposed a new voting system called the “Least Additional Members System”. Apologies for the clunky name.

Problems with first-past-the-post #

1. It is undemocratic in that “swing” voters in closely fought constituencies have orders of magnitude more influence than voters in “safe” seats
2. Issues that matter to people who happen to be distributed geographically (and don’t form a majority in any constituency) get ignored. These issues include gender equality, internet freedom and environmental protection.
3. Small political parties are forced into having a regional focus, because getting 500,000 votes in one constituency would give them a seat but 5,000,000 votes spread across India won’t. This has troubling implications for the country’s long-term unity.
4. Voters who think that their first choice candidate has a low chance of winning might vote for a less preferred candidate to avoid “wasting their vote”

Problem with vanilla party-list proportional representation #

In a large country, it is important that every geographic constituency is represented in the national legislature, which proportional representation cannot guarantee. An independent candidate who is supported by 51% of the people in a constituency but has no other support base won’t become an MP in a proportional representation system, which also has negative implications for national unity.

Requirements #

An ideal voting system must therefore satisfy two criteria:

1. Every constituency must be represented
2. Each party’s share of parliamentary seats must be proportional to its national vote share.

As a practical matter the procedure for voters must not be different from it is today. (This rules out ranking/transferable votes)

How it works. #

MPs representing constituencies are elected by the FPTP system as they are today. In addition, a variable number of additional seats are calculated after votes are counted and allocated to parties that are under-represented (in relation to their vote share) to make the overall parliament proportional.

As the number of additional seats depends on the outcome of the election, parliament has a variable (but bounded) size. This is unusual but I’m not aware of any reason for it to be a problem.

Before the election, parties submit a priority list of candidates to be considered for the additional seats. The list can include candidates who are also contesting in constituencies – if they win the constituency seat, their name will be removed from the list.

After counting votes, a national vote count for each party is tallied. For each party which won at least 2 constituences, the ratio R = constituencies won ÷ votes received is calculated.

The highest value Rmax is identified. This is the ratio for the most over-represented party in the FPTP system, and our goal is to give additional seats to other parties so that for every party the adjusted ratio R’ = (constituencies won + additional seats) ÷ votes received is as close to Rmax as possible.

Each party (including parties that won no constituencies), receive additional seats as given by Rmax × votes received - constituencies won, rounded to the nearest whole number. The total additional seats in parliament is approximately Rmax × total votes - total constituencies

Note that the proportionality is not perfect: parties that win just one constituency may be over-represented with respect to their vote share. This is a necessary trade-off to avoid an excessively high number of additional seats.

Back-testing #

At the time I did the original analysis, the latest available data was from the 2004 Lok Sabha Elections. The number of constituencies was 543, and applying the formulae resulted in 457 additional seats for a total parliament of 1000 members.

The highest FPTP anomaly in that election was the AIADMK, which received 2.1% of the total votes cast but won no seats. They would have received 21 additional seats under this system.

Implications #

1. More single-issue parties. I believe that a powerful new party focussing on gender equality and womens’ safety will emerge, as will smaller parties focusing on freedom of expression, the environment etc.

2. More diverse but more stable coalitions. Unlike coalitions of national parties, a coalition led by a national party in an alliance with many non-overlapping single-issue parties will be relatively stable. Several European countries work this way.

3. Two-horse races will open up. The “wasted vote” idea results in many voters simply picking from the two top parties in their constituency — without this phenomenon, smaller parties will get more votes and seats.

4. More uniform campaigning. Political parties will campaign throughout India and not just in tightly fought constituencies, because every vote will be worth approximately the same.