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# Voting matters - Issue 12, November 2000

## A Comparison of Electoral Systems using Decision Analysis

#### H G Jones

Bob Jones is a retired mathematician and former secretary Derbyshire Electoral Reform Group (DERG).

### Introduction

Decision Analysis is a method by which comparisons between different courses of action may be evaluated in order to obtain a desired end product. In the field of electoral reform the end product is the best electoral system, and the means of evaluating different systems is by comparing how well they measure up to desirable features of such systems.

The idea of applying Decision Analysis to electoral systems was first suggested by Tony Cooper, chairman of DERG,in the late 1980s and initially the performance of a system against each feature was evaluated as excellent, good, fairly good and poor. More recently the evaluation has been carried out numerically with scores being given up to a maximum of 10.

As well as this scoring procedure, it was realised that certain features were of greater importance than others, and weighting factors (WF) were therefore applied to each feature. For example, proportionality is considered to be very important and is thus given a WF of 3 , the relevant feature score being multiplied by WF. On the other hand ease of counting is not of great importance as the returning officer and his or her staff will have been trained to deal with the relevant system. In this case the weighting factor (WF) is taken as 1.

### Notation for systems

#### 1. Single Member Constituencies

• FPTP(SM): First-past-the-post.
• AV(SM): Alternative Vote.
• #### 2. Multi-Member Constituencies

• PL(MM): Party List based on the whole country (as in Israel).
• PLRC(MM): Party List based upon regions using a closed list.
• PLRO(MM): Party List based on regions with an open list.
• STV(MM): Single Transferable Vote.
• #### 3. Hybrid Systems

• AMS(HY): Additional Member System as used in Germany and in differing forms for the Scottish Parliament and Welsh Assembly.
• AV+(HY): AV(SM) with a top-up as proposed by Lord Jenkins for Westminster.
• AV+50(HY): Similar to AV+(HY) but having equal numbers of local and regional members.
• ### Notation for Features

• PRO-R: How proportional is the result within a region? (A region is visualised as, say, ten adjacent single-member constituencies).
• PRO-N: How proportional is the total election result? CHO-P: Is there a choice within a party as well as across party lines?
• ONECM: Is there one class of elected members?
• EASV: How easy is the system for the voter?
• EASC: How easy is it to conduct the count?
• EASBC: Does the system ease the task of determining constituency boundaries?
• EW&E: Does the system encourage women and persons of ethnic minorities to stand for election?
• LOC: How closely is the elected member linked to his or her constituency?
• PLOC: How easily can a voter contact an elected member of their own political persuasion?
• ### My Decision Table

#### 1. Weighting factors

The weighting factors I have chosen for the features above are:
• WF=3 for PRO-R, PRO-N, EW&E, LOC.
• WF=2 for ONECM, EASV, PLOC, CHO-P.
• WF=1 for EASC, EASBC.
• #### 2. Decision Table

The figures in parentheses are obtained by multiplying the score (out of 10) by the weighting factor WF, thus obtaining a weighted score. The total (weighted) score is the sum of the weighted scores for each feature of a system. The figures presented in the table gives my own judgement of the features for each system.

### Conclusions

On this basis STV appears to be the best system. This, however, is something I have believed for the last 20 years or so. Maybe I have been subconsciously biased!

The scoring and weighting reflects my personal opinions and feelings. Small differences in scoring and, particularly in WFs, can easily change the above conclusions and I would be grateful for other opinions.

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