Shiva Gautam, PhD Asst. Professor, Harvard Medical School, Harvard University, MA, USA

### ABSTRACT

Proportional representation system has been successfully implemented in several western countries and can be used for fair representation of minorities and ethnic groups.

### INTRODUCTION

Much of the national debate these days is focused on framing a new constitution and restructuring the state so that we can govern ourselves effectively and efficiently in the future. In order to govern ourselves, we need to elect a number of representatives at national, regional and local levels. Dissatisfaction over the past election system has been expressed by several quarters.

“One-man one-vote” and “winner-take-all” concepts have been the backbone of the current voting system. Lack of a built-in mechanism for a proportional representation has been one of the fundamental criticisms of this electoral process. For example, under this voting system, the proportion (percentage) of votes received by a party in an election is not often reflected by the proportion of seats won by that party.

In addition to above weakness, current one-man one-vote concept is inherently flawed from a certain viewpoint. A compromise between a somewhat philosophically idealistic sounding system and what is practical is being proposed. It is shown that this compromised system includes few forms of proportional representation (PR) voting system adopted by few democracies around the globe, and demanded by several in Nepal.

### Basic electoral units

The country of Nepal belongs to every Nepali equally. So, theoretically, each Nepali should directly take part in running the country. Since this is almost impossible, we may opt for an alternate of electing few representatives and asking them to run the country as our proxies.

Suppose we, as a nation, decide that there should be one representative per 100, 000 people. If the total population of Nepal is assumed to be 28,000,000, then we need 280 elected representatives to run the country. Let a collection of 100,000 people (often living within a contiguous geographical area) be called a basic electoral unit. Then Nepal will have 280 basic electoral units, and the proposed legislative body will have 280 seats.

The 280 representatives, can be elected using one-all, one-one and one-many systems defined below.

### One-voter, all-votes (one-all) voting system

I define one-all system to be the one where each voter has as many votes as there are seats in the legislative body. Continuing with the hypothetical example of 280-seat legislative body described above, it only makes sense for each Nepali to vote directly for all 280 candidates of his/her choice. Again, the basic idea behind this argument is that each and every Nepali has an equal stake in Nepal. Thus, under the proposed one-all voting system every voter has 280 votes (equal to the number of seats) at his/her disposal.

A voter may prefer a candidate over others or he/she may prefer a political party. Obviously, a voting system that allows a voter to use or distribute his/her votes (280 in this case) in anyway he/she wants is seems reasonable. Using such preferential voting is equivalent to assigning certain weights to candidates. So if a voter assign 100% weight to a candidate, then the voter will cast all his/her votes to the candidate.

This further allows a voter even to cast fractional votes (1.5 votes, 2.33 votes, etc.). Expressing a preference of 1, 2, 3 …280 is equivalent to fractional voting with 1.993 and 0.007 votes (out of a total of 280) to the most and least preferred candidates, respectively.

If preferences 1, 2, 3, …, N ( N = total seats, 280 in our example) are used as weights (in decreasing order) then the number of votes for the ith choice = [N x (W i / Sum of weights)]. In our example the ith weight, W i = (N + 1– i). In real life situations it is lot simpler to indicate first preference, second preference using numbers 1, 2, 3 and so on through a ballot paper than to use fractional votes like 1.993 and 0.007.

The proposed one-all system, however, will be very cumbersome logistically, impractical for various reasons and we are not perhaps ready to take such a leap yet. I sincerely hope that one day all citizens of a country will be able to directly vote for all representative at the national level under the one-many voting system.

### The one-voter, one-vote (one-one) voting system

In this system, a voter has only one vote as contestants compete for a single seat. Elections held within a single basic electoral unit naturally fall under this classification.

All elections held from 1960’s to date for different forms of legislative bodies in Nepal that used winner-take-all voting systems were basically one-one systems. It is already mentioned above that the system does not guarantee proportional representation.

Note that, one-all system reduces to one-one systems when a basic electoral unit is treated like a country in itself with a one-seat legislative body. If one-all system is an ideal system at one extreme of the representation scale, then one-one system lies at the opposite extreme. In the case of 280 seats legislative example, about 99.6% of the population will not be involved in the election of a candidate elected to the national legislative under the one-one system.

### One-voter, many-votes (one-many) voting

In one-many system, a voter has several votes but not all the votes as in one-all voting system. Under this system several basic units are combined and each voter within the combined area has as many votes as the number of basic units included in the combination.

Suppose that five basic electoral units (each with 100,000 people) are combined. Then this combined geographical area will vote for five seats and each voter will vote for five candidates of his choice.

Note that one-many system becomes one-all for a regional legislative body’s election if all the basic electorate units in the regions are combined. While one-one and one-all are at opposite ends of an electoral system, the one-many system is a compromise between the two. Thus, it may still not be an ideal system but is certainly an improvement over one-one system.

The same candidate may be elected using any one of the voting system discussed here, but the implied participatory significance and value will be enormously different.

One can extend the areal definition of a basic electoral unit to other characteristics or combination of characteristics (e.g. gender, ethnicity) of the population.

Since we are so used to these one-one systems, a concept of one-many system (one voter, many votes/seats) may even sound unethical initially. However, proportional representation voting system adopted by many democracies in the world could be considered on-many system of election where one voter votes directly indirectly for several candidates (seats).

### How many Basic units to combine?

Assuming that all 28,000,000 people in our example are eligible to vote, the maximum possible number of disappointed people for not seeing their candidate elected to the parliament will be 13, 999,720 (approximately 50%) under one-one system. However, under the one-all system, no more than 99,400 (less than 0.4% or 4 in 1000) will be disappointed or not represented. If the country is divided into 28 areas each consisting of 10 basic electoral units, then no more than 3.4% of the voters in the country will be disappointed.

Instead of measuring in disappointment, we could measure the possible results in its complement Let us call it Participatory Index (PI). Thus in one-system (elections held without combining any basic electoral unit), PI = 50. Similarly, PI = 99.6 and 96.6 when all units are combined (one-all system) and 10 basic units combined, respectively.

The following graph shows relationship between numbers of basic electorate units combined and the PI.

The graph shows that initially participatory index (PI) increases exponentially, but after sometimes it starts to level off. The PI jumps to 80 from its minimum possible value of 50 when 4 basic units are combined. The PI = 90 when 9 units are combined, and increases to 95 when 19 units combined. We have to add 14 additional units (i.e. 33 basic units) for additional 2 units increment in PI (= 97). So it seems that, a combination of 4 to 9 units may be ideal under the assumptions (e.g. number of total voters, definitions of basic electoral units).

Let C be the number of basic electoral units combined to elect of C candidate from the combined area. Then the maximum number of disappointed voters (approximately) = [(total voter in the combined area)/(C +1) – C]. If the whole country is divided into areas consisting of equal number of basic electoral units, then the maximum number possible disappointed voters (approximately) = total seats x [basic electoral unit population/(C + 1) – 1]. It can be shown that PI = 100x[C/(C + 1) + 1/K], where K is the size of a basic electoral units.

### Proportional representation (PR) voting systems

There is a lot of information out there about proportional representation. I will briefly highlight few important features of PR.

As mentioned above, several forms of proportional representation systems are in fact one-many systems articulated in this piece. For example, under the one-many design we could elect five representatives from an area with a population of 500,000 people. As a simple example, each political party could nominate up to five candidates for this five-member basic electoral units. A voter can elect up to five candidates of his or her choice. So, a voter will have five direct or indirect votes.

The actual process should be determined by consensus by the leaders and experts. In one of the simplest for of PR election, each political party may or may not provide a candidates’ list. A casts all his votes to his/her party of choice. Independent candidates are treated as separate parties. Then the percent seats won by a party are the percent of votes received by that party. A ballot for 3-member basic electoral units may look like as follows (just an example):

BALLOT PAPER (example only) | ||||||
---|---|---|---|---|---|---|

NC | Janamorcha | CPN(UML) | NC(D) | CPN(M) | Sadbhavana | RPP |

Mr. A | Ms. D | Mr. G | Ms. J | Mr. M | Mr. P | Mr. S |

Ms. B | Mrs. E | Mr. H | Ms. K | Ms. N | Mr. Q | Mr. T |

Mr. C | Mr. F | Mr. I | Ms. L | Mr. O | Mr. R | Mr. U |

Note that under the above plan each voter checks one box only and thus selects three candidates from a party of his choice.

Suppose that NC receives one third and RPP receives two-thirds of all the votes, then Mr. A or any other one candidate from NC according to prior arrangements is elected and remaining two seats will go to RPP.

There are several variants of the voting system. In one of the alternate system a voter is allowed to choose candidates as well as party of his liking. Yet in another system, a candidate is allowed to distribute his votes (equal to number of seats) over the candidate in any way he/she wants. In this system, a candidate may even cast all his votes to one single candidate.

One interesting system within proportion representation uses a method known as ‘single transferable vote’. In this system a voter may express his/her first choice, second choice, third choice and so on up to number of seats to be filled. A candidate must receive votes equal to a quota (often called Droop Quota) computed as Quota = [total votes/(seats+1)] + 1. In the case of current single-member (one seat) or one-one voting system, this formula tells that a candidate must receive 50% plus 1 vote to win. In a three-seat constituency a candidate must receive 33.3% plus 1 votes to win. Votes received by a candidate in excess of the winning quota are transferred to other candidates according to a simple algorithm. Similarly, too few votes received by candidates are also transferred to other candidates. This algorithm will finally yield the required number of winners (equal to number of seats). This might sound complicated, but is very simple.

There are also few semi-proportional or mixed proportional representation voting systems that may be considered in between winner-take-it all and proportional representation system.

Proportional representation system has been successfully implemented in several western countries. This system can be used for fair representation of minorities and ethnic groups. Suppose that 25% of the population is of certain ethnic group. If they all vote for their candidate in a four-seat district, then the candidate from that particular ethnic group will win one seat, because she/he will have 25% (or one-fourth) of the votes.

Proportional representation system also avoids gerrymandering. In 1996, US Supreme Court declared few congressional districts that were created for minorities unconstitutional. If we are to learn from others experience then proportional representation could be a good alternative to the current voting system in Nepal

There are several forms of proportional representation. It is up to the leaders, legislators, legal experts, and members of civil society to choose an appropriate form for PR. There is also the question of representation of women and ethnic minorities. Representation of these groups could be addressed within or without the framework of political parties.

Biography of Dr. Gautam

Dr. Shiva Prasad Gautam is a faculty at the Harvard Medical School, Harvard University, MA, USA and can be reached at shivagau@gmail.com.