The 2007 Party-List Election in Japan

courtesy of http://www.sangiin.go.jp/eng/index.htm

Last Sunday, July 29, 2007, Japan held an election for the House of Councillors (Senators) which is the upper chamber of the Japanese Parliament or the National Diet.

A total of 121 seats were contested where 73 seats will be filled in forty-seven prefectural districts and 48 seats will be allocated by proportional representation on a national basis.

Every voter has to cast two votes for the National Diet. The first vote is for a single candidate in a prefectural district. The candidates with the largest number of votes in each district, up to the number of seats to be filled, are elected to office. The second vote is for the party-list system. The 48 seats will be allocated by the Highest Average Method devised by the Belgian Mathematician Victor D’ Hondt.

All the elected Senators will serve for 6 years. The total number of members in the upper chamber is 242 and half of them are elected every three years.

Seven parties are qualified to receive a party-list seat. These are:

1. Democratic Party of Japan (DJP) with 23,256,242 votes
2. Liberal Democratic Party (LDP) with 16,544,696 votes
3. New Komeito Party (NKP) with 7,762,324 votes
4. Japanese Communist Party (JCP) with 4,407,937 votes
5. Social Democratic Party (SDP) with 2,637,716 votes
6. People’s New Party (PNP) with 1,269,220 votes
7. New Party Nippon (NPN) with 1,770,697 votes

The total number of votes of all qualified parties is 57,648,832 representing 97.853050% of all the votes cast for the party-list. The qualified parties received all 48 party-list seats available.

The Highest Average Method

In the Highest Average Method, successive quotients or averages are calculated. It is determined by dividing the number of votes of each party by a sequence of integer divisors 1, 2, 3, 4, and so on.

The list of successive quotients for each qualified party using the divisors from 1 up to 25 is given in the table below.




The top 48 quotients shall determine the 48 seats to be allocated. Hence,

1. Democratic Party of Japan (DJP) shall be awarded with 20 seats,
2. Liberal Democratic Party (LDP) with 14 seats,
3. New Komeito Party (NKP) with 7 seats,
4. Japanese Communist Party (JCP) with 3 seats
5. Social Democratic Party (SDP) with 2 seats
6. People’s New Party (PNP) with 1 seat, and
7. New Party Nippon (NPN) with 1 seat

The table below shows the rank of each quotient corresponding to the seat number that each party obtained.


Analysis

The Highest Average Method allocates the total number of available party-list seats. The seat allocation error  is zero as well as the degree of negation. This means that the Highest Average Method affirms the principle of proportional representation on the parties participating the 2007 Japan party-list election. See table below.

where
TQPV is the total number of votes of all qualified parties,
Actual Number of Seats is the actual allocation of the
                 Highest Average Method,
Ideal Number of  Seats is the obtained by the product
                  of the  % Based on TQPV and 48, 
Seat Allocation Error is the Ideal Number of Seats 
                    minus the Actual Number of  Seats, and the
Degree of Negation is the absolute value of the integer 
                    part of  the Seat Allocation Error.

The index of proportionality of a given method is determined by dividing the sum of the absolute value of the seat allocation error by 96 and the result is subtracted from 1. A value of 1 or 100% means full proportionality and a value of 0 means a disproportionate method. The index of proportionality of the Highest Average Method on the 2007 Japan party-list election is equal to 97.088495%.