Jacob Block
Jacob Block

Recycling, Reweighting, and Recasting Votes: Israel and Gregor-Wright Voting

Israel uses the Bader-Offer method to apportion seat in the Knesset, but its time for a change. (Photo by Rafael Nir on Unsplash)

The following article assumes a basic knowledge of closed list proportional representation.

The Israeli electoral system has a problem: it wastes votes. It does this in three ways: firstly, and most notoriously, by not counting votes cast for parties that do not reach the electoral threshold for representation in the Knesset; secondly, it wastes votes by apportioning seats by using a ‘list indicator’, which I will explain in detail bellow; and thirdly, and most rarely, the Israeli election system wastes votes by not counting those votes cast for parties that do not have a long enough party list to be apportioned the number of seats they’ve earned. However, each way in which the Israeli electoral system wastes votes can be resolved. By altering the Israeli electoral system from the Bader-Ofer method  it currently uses to the Gregor-Wright method, every vote cast can be made to count.

The first change switching from the Bader-Ofer to Gregor-Wright method of voting would make to Israeli elections is to have Israelis not vote for only one party, but to rank every party on the ballot from their first choice to their second to last, leaving their last choice and those parties the voter isn’t familiar with unranked. Once the voters have ranked their ballots, each ballot will be counted and apportioned according to whichever party is ranked first on each ballot.

Starting with that party with the least number of votes of those parties that do not meet the electoral threshold, that party will have those ballots apportioned to it recounted and recast for whichever party each ballot ranks next. This process will continue until every party originally bellow the electoral threshold has been risen above it by the addition of transferred votes or been eliminated and had their votes transferred away. If the party a given ballot ranks second has, like the party it lists first, already been eliminated by not reaching the electoral threshold, the ballot is again recast, this time for the party ranked third, and so on.  Through this change, votes cast for parties that do not meet the minimum electoral threshold for representation in the Knesset will not be ignored but merely recycled.

The second change implementation of the Gregor-Wright voting method would make to Israeli elections is to carry out a process of ‘reweighting and recasting’ votes. In the current Israeli electoral system when a party receives 4G votes, where G is the number of votes referred to as the ‘general indicator’ and is ‘the sum of votes cast for those parties that overcame the electoral threshold divided by 120(the number of seats in the Knesset)’, that party receives 4 Knesset seats. When a party receives exactly 4G votes it is clear that they will receive four Knesset seats. But what happens when a party receives 4G+S votes where S>0 and <G and stands for ‘surplus votes’. If each party that receives XG+S number of votes is apportioned only X Knesset seats, the sum of Knesset seats allocated to each party will be less than 120, and so there must be a way to apportion the remaining seat(s). The current Israeli election system uses a ‘list indicator’ as prescribed by the Bader-Ofer method to apportion unfilled seats. Bellow I paraphrase an explanation of this ‘list indicator’ method as it appears on the knesset.gov.Il website. (The following excerpt is not an exact quote but rather altered slightly for comprehensibility within the context of this article).

The problem of unapportioned Knesset seats and of parties’ surplus votes (S) is resolved by dividing the total number of valid votes given to a list (XG+S) by the number of seats given to that lists(G) plus 1 (XG+S/G+1). The reason for adding 1 is for determining what the ‘list indicator’ would be if the party would receive that additional seat. The list with the highest ‘List Indicator’ receives the surplus seat. The ‘List Indicator’ for additional seats will be calculated based on the new distribution (i.e. plus 2 for the lists that already received a seat, and so on). These calculations are continued in this way until all surplus seats are distributed.

Basically, this means excess Knesset seats will be distributed in proportion to a party’s share of the sum of parties’ surplus votes.

What the Bader-Ofer method’s use of such a ‘list indicator’ to apportion seats gets wrong is that it ignores the surplus votes of those parties (and party alliances) that do not have a large enough S value to be apportioned extra Knesset seats.

This problem can be resolved by the process of ‘reweighting and recasting’ included in the Gregor-Wright method. Starting with the party which receives the lowest S value, all votes for that party shall instead be reweighted according to the formula ‘S (surplus votes received by that party)/ XG+S (total votes received by that party where G is the total number of votes cast for all party’s divided by 120 (the number of seats in the Knesset))’. Next all these reweighted ballots cast for that party are recast for the next ranked party listed by each voter on their ballot with each ballot counting not as one vote but some percentage of one vote as determined by the reweighting formula. This process continues for each party from that with the lowest number of surplus votes (S) to that with the highest, with each round a ballot is reapportioned causing that ballot to be worth a fraction of the vote value it was in the previous round. When there are only two parties left capable of being apportioned  extra seats, the Bader-Ofer’s ‘list indicator’ method referenced above shall be employed. Through this process of ‘reweighting and recasting’, no votes are wasted so long as every voter is required to rank every party running, and no S value is too small that those votes which make it up won’t count towards a Knesset seat; all votes will matter.

The ‘Reweighting and recasting’ method of vote allocation also solves the third way by which the current Israeli election system wastes votes: if a party receives an X value larger than the number of candidates on their party list, all those votes cast in addition to those which constitute an XG value where the X value is equal or less than the number of candidates on the party list will be wasted as that party can not be allocated seats in the Knesset they do not have candidates to fill. Such a case has only occurred once: in the 1977 elections the Flatto-Sharon party, which had a list made up of only one man, the eponymous Shmuel Flatto-Sharron, received 2G+S votes and so if it’d had a longer party list would have been entitled to twice as many seats in the Knesset as the one it ended up receiving. Because votes cast for party lists which are not long enough to absorb them are wasted, Israeli political parties almost always make sure their lists have more candidates than the number of Knesset seats they are expected to win.

By employing the Gregor-Wright method’s system of reweighting and recasting, a party list can be as short as that party wishes: if a given party receives an X value greater than the number of candidates on its list, the number of candidates on its list is subtracted from the X value, the result is multiplied by the G value, and added to the S. This new value, which I will refer to with the variable N, is divided by the number of total votes cast for that party (N/XG+S) in order to determine how each vote will be reweigted before being recast.

Some may ask why any party would want to give up political power in the form of more seats in the Knesset by truncating their lists. The answer is that large political parties can be both unwieldy and impersonal. Political  party’s in Israel often see defections of their members and are sometimes less popular then their major exponents. A smaller party may be both more internally stable and electorally reliable. However in the current Israeli electoral system, parties aren’t enabled to find out, as any vote cast for them which does not count towards a Knesset seat is a vote not cast for those parties that are ideologically aligned. A similar logic informs why voters in the United States rarely vote for third parties.

Implementing these changes to Israeli election law would make the results of Israeli elections much more representative of the people’s will. However doing so also has drawbacks. For one the repeated process of reweighting and recasting votes would drastically increase the amount of time it takes to tally election results. This problem can be resolved by the computerization of the vote counting process. Though such a digitization may cause many to worry about an increased susceptibility of Israeli elections to interference from hackers, if block chain technology is employed in tandem with such a digitization, the cause for concern should be little.

Another problem with the Gregor-Wright method is that each round of reweighting a ballot goes through causes the ballot to take on a smaller and smaller fraction of its original worth of one vote, and so the recasting of ballots will often involve the recasting of ballots which are of such a small value they have no significant effect on the election results. As such, the calculations involved with reweighting ballots will often involve long irrational numbers and it is presumable that to simplify the process and or save time some small arbitrary value shall be set bellow which a ballot is discarded rather than recast. Though always to some degree necessary, the inclusion of any arbitrary value in electoral calculations injects a certain degree of arbitrariness into those calculations’ results: something that hurts citizens’ perception of the representativity of their elections. However the values subject to this rounding process will be so small it is exceptionally unlikely to actually make a difference to the results of an election and so is also exceptionally unlikely to actually hurt elections’ representativity.

Another and obvious weakness of the Gregor-Wright voting method is that, like all ranked choice instant runoff voting systems (also known as ‘Single Transferable Vote’), it asks voters to be familiar with and have opinions on all the candidates/parties on the ballot. Though such a familiarity is the ideal in all democracies, most function such that a voters need only know of one candidate/party that they are willing to see put in power. Though being familiar with every party on the ballot may be a big ask for most, there are few countries with electorates as politically engaged as Israel’s, and so few so up to the task. (A Pew Research ranking of 35 developed nations places Israel as 8th in terms of voter turnout based on those countries’ most recent significant election. For reference The United States was ranked 30th). Further it is not actually required that a voter rank every party on their ballot, only that they do so if they want to maximize their electoral influence; a voter can rank only two parties if they wish; they can ‘rank’ only one.

However, such an allowance has draw backs of its own. The final fault of the Gregor-Wright system as I’ve laid it out is that the more voters to rank fewer parties the greater the chances that more seats than the minimum one will be in contest between the last two parties during the last round of seat allocation during which the Bader-Ofer list indicator is used. This means that if a large portion of the electorate were to not rank a  large portion of the parties on their ballots, there is a chance that the two final parties would end up with an unrepresentatively large portion of seats in the legislature. To decrease this possibility and its severity if occurrent, Israel may find it useful to mandate that each voter ranks, if not all, a large minimum number of the parties on the ballot.

Even with its draw backs, using the Gregor-Wright voting method to conduct Israeli elections would be a major improvement on the current system. It is unfortunate then that this method is unlikely to be implemented in Israel, or indeed widely implemented elsewhere. Apart from being rather esoteric and so hard to create a popular understanding of and so support for, successful implementation of such a major change to the constitution of an established democracies is rare (the ongoing Chilean constitution convention being possibly such a rarity), in large part because reforming the structure of a democratic state requires the consent of those empowered by that incumbent structure. . New ideas about government often have to wait for implementation until the known world has been turned upside down, as during decolonization, or expanded, as during colonization. As I’m not expecting a global revolution any time soon, I believe that if this idea for an improved electoral system is ever to be widely implemented, it will not be as an actual improvement to the Israeli or any other state, but as the brand new electoral system adopted by a brand new state. I’m looking at you space colonists.

To be clear the voting method I refer to above as ‘Gregor-Wright’ is a slight alteration from ‘Gregor-Wright’ as it’s traditionally described. Further, Gregor-Wright is usually not referred to as one system but two: the Gregor method (also known as the ‘senatorial method’ and named for the Senate of Northern Ireland which is the only legislature in the world currently to use it to elect its members) and the ‘Wright method’ which is understood as an alteration on the Gregor. However whatever their slight differences in name and substance, the system I advocate for Israel and that described elsewhere share their essential characteristics: chiefly among them, their capacity to make elections more representative of the communal and ideological diversity of their electorates. Something a state as polyphonic as Israel could use.

About the Author
Jacob Block was born in 1999 and lives in Saratoga Springs, NY.
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