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Tom Monto

Demonstration STV election - party food sample STV election

Updated: May 23, 2023

Example for a non-partisan election

Suppose an election is conducted to determine what three foods to serve at a party. There are seven choices: Strawberry donuts, Pears, Strawberries, Cake (Strawberry-chocolate), Chocolate, Hamburgers and Chicken. Only three of these may be served.


There are 23 guests, and the hope is that each guest will be served at least one food that they are happy with. It is decided to use STV to make the decision. Each guest is given one vote but is also allowed to cast two optional back-up preferences to be used only if the first preference cannot select a food or to direct transfer of surplus votes if it does. The 23 guests at the party mark their ballots with first, second and third preferences.


When the ballots are completed, there are nine distinct combinations, as shown in the table below.


The various ballots as marked

1st preference 2nd preference 3rd preference

Strawberry donuts Strawberries 4

Pears Strawberries Cake (strawberry) 7

Strawberries Cake (strawberry) Pears 1

Strawberries 1

Cake (strawberry) Strawberry donuts Strawberries 3

Chocolate Cake (strawberry) 1

Hamburgers Chicken Hamburgers 4

Chicken Hamburgers 1

Chicken 1


The table is read as rows:

The top row shows that there were four ballots with Strawberry donut as the first choice, and Strawberries as second.

The bottom rows show there were two ballots with Chicken as first choice (one of them has Hamburger as second choice).


The election round by round:

first calculate the quota, the number of votes that guarantees election


Setting the quota

three to be elected.

The quota is 6 23/(3 +1) rounded down and 1 added



First Round

count votes for each candidate

Donuts Pears Strawb. Cake chocolate hamburgers chicken

4 7 2 3 1 4 2

ELECTED

(1 surplus vote)



Round 2

transfer surplus votes

4 ELECTED 1 +1=2 3 1 4 2

(6 votes)



Round 3

4 ELECTED 2 3+1=4 eliminated 4 2

(6 votes)



Round 4

4 ELECTED eliminated 4 0 4 + 2 = 6 0 4 2

(6 votes) ELECTED

(6 votes)

(0 surplus votes)



Round 5

4 ELECTED 0 4 0 Elected 4 + 1 = 5 eliminated

(6 votes) (6 votes)


after Round 5

eliminated ELECTED 0 4 0 Elected 5 0

(6 votes) Elected


Result

Pears ELECTED in First Round

Cake elected in Round 4

Hamburgers elected after Round 5.


Setting the quota: The Droop quota formula is used, giving Quota = total votes / (options to choose + 1) + 1, rounded down = 23 / (3 +1) rounded down = 5.75 rounded down = 5. add 1 = 6.


Round1: First-preference votes are counted. Pears reaches the quota with 7 votes, and is therefore elected on the first count, with 1 surplus vote


Round 2: All of the voters who gave first preference to Pears preferred Strawberry next, so the surplus vote is awarded to Strawberry. No other option has reached the quota, and there are still two to elect with six options in the race, so elimination of lower-scoring options will start on the next round.


Round 3: Chocolate has the least votes and is eliminated. According to their only voter's next preference, this vote is transferred to Cake. No option has reached the quota, and there are still two to elect with five in the race, so elimination of options will continue next round.


Round 4: Of the remaining options, Strawberry and Chicken now have the least votes. Of the two, Strawberry has fewer first preference votes so is eliminated. According to the preferences of one of the two voters who voted Strawberry, and the voters of Pears who gave the surplus vote to Strawberry, two of the Strawberry votes are transferred to Cake, which reaches the quota and is elected. But Cake has no surplus votes. No other option has reached the quota, and there is still one to elect with three in the race, so elimination of options will continue next round.


Round 5: Chicken has the least votes and is eliminated. Only one of the three votes carries a back-up preference. According to that Chicken voter's next preference, this vote is transferred to Hamburgers.


After Round 5:

Hamburgers is elected because Strawberry donut has fewer votes. Hamburgers is elected although it does not have quota. There are no more seats to fill. The votes for strawberry donut (plus the "exhausted" votes initially marked for Strawberry and Chicken) are the only votes that are wasted, the only voters who are ignored.


Result: The winners are Pears, Cake and Hamburgers.

STV in the demonstration election produced a higher number of effective votes – votes used to elect the successful candidates: 14 voters saw their first preference chosen, and the 9 others saw their second preference served.

Compared to other systems

This result differs from the one that would have occurred if the three winners were decided by first-preference plurality rankings (single non-transferable vote (SNTV)), in which case Strawberry donuts would have been a winner, as opposed to Cake, for having a greater number of first-preference votes.


Under SNTV, 15 voters would have seen their first preference win (Strawberry donuts, Pears and Hamburgers), the other 8 would not have seen their first choice served. Three of them would have seen their 2nd preference food served (this would not have been marked so would likely not have been known). Five voters would have none of their favorite foods served.


Under first-past-the-post (FPTP), the guests would have been split into three groups with one food chosen by each group just the most popular food preferred by each group of voters' first preferences. The result in this case would have been dependent on how the groups are formed. Gerrymandering of the groups to bias the election toward a particular result might occur. The winners might have been Strawberry donuts, Pears and Hamburgers, but also the foods chosen might have been Pears in two groups (districts) and Hamburgers in the other. Or even just Pears alone might have won in each of the three "districts", in which case only 7 guests out of 23 would have seen their choice served, a very unrepresentative outcome, given that three different foods could have been served.


Similar problems arise to a lesser degree if all districts use a majority system instead of plurality (for instance, two-round or instant-runoff voting) as at least in all districts the majority would have been quite happy, but that still leaves the minority unrepresented.


It could also happen that none of the groups elect Pears, because the 7 votes for it might be split and in each of the "districts" there might be another food that beats it (e.g. Strawberry donuts, Hamburgers and Chicken).


If the voters had been able to choose only one food to serve (as in first-past-the-post, but without "districts"), it is likely that Pears, the choice of less than a third of the 23 party-goers, would have won, meaning Pears would be the only food served at the party.


Even if they held two rounds of voting, with one winner, the nine voters who prefer some kind of strawberry dish) would have dominated all other choices.


If the election had been held using Block voting, likely Strawberry would have won and been the only food served, although there were potentially three different foods served. The result produced by the STV election above was not simply result of giving voters more votes (in fact STV is single voting), and Block voting, where votes cast multiple votes, does not actually produce a more fair result or ensure that more votes are happy with result than single voting under STV. Giving electors a single transferable vote is very different from simply giving each voters more votes to cast. Block Voting, where each voter is given as many votes as there can be winners, is called plurality block voting. It can produce very unrepresentative results.


A single group with only a minority of the votes could pick all the winners if it is larger than any other single group. Being able to cast multiple votes means that a group would not need to worry about vote splitting due to too many candidates in the running (unless the group runs more candidate than there are seats).


In the example above, if every voter could vote for three options, the group of voters who chose a strawberry or a strawberry dish could easily force all three outcomes to be strawberry related (strawberries, strawberry cake or strawberry donut): an outcome that is unlikely to be more representative than each voter simply casting one vote. In the example above, where no faction commands an absolute majority, the largest of the minority groups can force a one-outcome result by running clone candidates - various strawberry dishes.


The nine lovers of strawberry arranged in advance to have three types of strawberry foods included on the ballot, then cast all their votes for the three, and if no other option is more popular than the "strawberry" slate (candidates on that slate could take 9 votes each if strawberry lovers vote along slate lines), the three foods served would be three types of strawberry. The only way this could be avoided would be for those who do not like strawberries, or at least ten of them, to vote tactically, by not choosing their various preferred options, but instead all moving to support the same three non-strawberry candidates - whatever they consider to be the least bad alternative to strawberries that is likely to gain enough votes to be elected, the best chance non-strawberry contender. But if that voter discipline is not pursued, the Strawberry coalition will see three strawberry dishes served and no others.


blogger's editorial note

(I tried to get this demonstration election on the Wikipedia article "Single transferable voting" but it was undone. so here it is anyway if anyone sees it!


This election has exhausted votes, has one candidate elected without quota and presents slate idea with three strawberry foods.

all potential outcomes under STV.


As well, one change made when the Wikipedia article went to new demonstration election was to ensure that it was set up in such a way that more voters were satisfied under STV than SNTV. That is good change.


But we also want to show that SNTV may allow more first preferences to be elected than STV, but STV ensures that more see either their first or second or third preference elected than see their first preference elected under SNTV.


Most but not all candidates in winning positions in the first round of STV election are elected in the end. Any who are not are replaced by those who had support of fewer voters in Round 1. so the final result under SNTV does satisfy more voters than votes as cast in Round 1 of a STV election.


But STV election results satisfy more voters if we look at back-up preferences marked on ballots initially cast for initially-less-popular candidates.


The new example does show that Oranges, one of the leaders in Round 1, is not elected at the end, while Cake, initially less popular, picks up vote transfers from Chocolate and from Strawberries to accumulate more votes than Oranges and win.


Oranges meanwhile is back-up preference of no voters (or at least none so marked are put into effect), so never does get quota or be leading when the field of candidates thins to the number of remaining seats in Round 5.


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SUGGESTIONS


for voting

make sure each "district" has about same number of votes by say having five votes available for each and only after all 25 of those have been issued, five to each district, start to give out next round of votes, next group being maybe three for each district, and so on. if that makes sense


for vote counting

first announce the results as per the first preference, with candidates listed in order of popularity (number of first votes received)

already any candidate(s) with quota are known to be elected.

the one at the bottom is certain to be eliminated


audience is told that:

those at the bottom are likely to be eliminated

those near the top are likely to be elected.

and that the vote count and vote transfers will determine the exact results.


And I think do the vote transfers in front of the audience.

but if not, announce the results round by round as the vote count progresses

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