Four Easy Analogies to Understand BC-STV
Here are four easy ways to understand how STV works:
1. Choosing Captains for Gym Class
2. Eating Chinese Food
3. Easy as Pie - Choosing Pie Fillings
4. Choosing Ice Cream Flavours - Your Vote is Like a Dollar
1. Choosing Captains for Gym Class
Imagine that your gym class is going outside to play a game and that your teacher wants to divide you up into four teams. The teacher asks anyone who wants to be a team captain to stand along a line. Let's imagine that about 8 kids volunteer to be a captain, so we have to find a way to cut this group down to only four (these are like the candidates in an election).
The teacher then tells the rest of you to go stand behind the kid you'd like to be your captain. If there aren't enough kids standing behind any of the candidates to form a team, then the teacher will go to the smallest line and tell the would-be captain that they don't have enough players, so they'll have to step aside. The teacher will then tell all the kids in that line to find another team they want to be part of - each kid will then go to their second choice.
If a captain is particularly popular, they might have more than a full team's worth of players lined up behind them, so the teacher will tell them that the excess players will have to leave and find another team to play with.
These two steps repeat until each player is on one of the four teams.
Interpretation: each player is like a voter. They get to say what their first choice is, but if they can't have their first choice, they can try their second choice. In the end, almost everyone is on a team that they want to be on. This example illustrates most of the main ideas behind BC-STV, but there's one additional feature of STV that's not captured here. See example 3 for more about this.
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2. Eating Chinese Food
Imagine that you and 20 of your friends are going out to eat Chinese food. You're seated in groups of seven at three different tables. Suppose that this restaurant is only going to serve you all three dishes - one for each table.
If you chose your dinner using First Past the Post, each of you at a single table would vote for your favourite dish. It might be the case that at your table, three of you chose Kung Pao chicken, two chose Moo Shu pork, one chose Spicy Green Beans, and one chose Shrimp Fried Rice. Kung Pao chicken would win, and the restaurant would serve your table one large platter that all of you would have to eat.
If you chose your dinner using BC-STV, all 21 of you would write down on a slip of paper what your first, second and third choices were (and as many others as you'd care to specify). Since you'll collectively be served three dishes, if any 6 of you choose a dish, it will be served (since there can be a maximum of three sets of 6 people in your group of 21; if four dishes were served, if any five of you agreed, a dish would be chosen).
Imagine that all the options are laid out on a side table. Each of you puts your slip of paper beside your first choice. If no dish has six slips of paper in front of it, the dish with the fewest slips is taken back to the kitchen and all the ballots that named that dish as the first choice are moved ('transferred', as in Single Transferable Vote) to the next choice indicated on each slip. If a dish has more than 6 slips in front of it, the excess slips will be moved to the next choices marked on each slip, as with the captain selection example above.
Interpretation: The different dishes are the candidates. With First Past the Post, everyone has to 'eat' the same dish, whether or not they like it. They can't eat the other dishes because they're served at different tables. With BC-STV, almost everyone ends up with a dish they like, and they can eat it because it's served at a shared table.
3. Easy as Pie
Imagine all the members of a social club were asked to work together to make some giant pies to be served at a homeless shelter event. These pies are so big they'll require 20 cups of flour each - these are big pies!
Each member is asked to bring one cup of flour and they’re allowed to pick which pie they wish to contribute to. A number of donors have offered to contribute the pie filling, and they've all shown up with their proposed filling in a big jar which they've placed on a table alongside a big 20 cup bowl. If they can collect 20 cups of flour from the club members, they get to bake their pie.
Interestingly, there seem to be three main types of pie filling offered - fruit (blueberry, raspberry, apple, etc), cream (lemon meringue, coconut cream, etc) and holiday types (pumpkin, pecan, etc). You can think of these types of fillings as analogous to political parties and the specific fillings as analogous to candidates.
When the choosing starts, the club members gather around their favourite fillings. Let's say blueberry pie is really popular and there are 30 people lined up to contribute their cups of flour. Since only 20 cups are needed, each club members only empties 2/3rds of their cup into that bowl, and they can then take their remaining 1/3rd cup to their next choice.
If a pie filling is not that popular (say raisin pie, with all due respect to raisin-pie-lovers out there), then there might only be 3 or 4 club members standing around that pie filling's bowl. The club organizer will come along and ask them to take their cup of flour to their next favourite filling.
This process repeats until there's less than 20 cups of flour left amongst all the club members who haven't used up all their flour.
Interpretation: Each pie filling is like a candidate, each club member like a voter, and each cup of flour like a vote. Each voter has a chance to show their support for their favourite candidate, but if they're not popular enough to be elected, the voters can go on to their next choice. If a candidate is really popular, each voter who supports them only has to contribute a portion of their vote to elect that candidate, and can give the balance of their vote to another candidate they support. In this way, each vote is used to it’s maximum. Thanks to Liquid Thoughts for this analogy. I have shamelessly borrowed from it here.
4. Choosing Ice Cream Flavours - Your Vote is Like a Dollar
Imagine that your soccer team has 21 players on it and you're all going out for ice cream after a game. Suppose the store doesn't have individual cones, but has 1 litre containers available instead for $6/litre and that each container will make about 7 ice cream cones. Let's also say that there are 12 flavours available:
- 3 white ice creams - vanilla, coconut and french vanilla,
- 3 brown ice creams - mocha, chocolate and espresso,
- 3 fruit ice creams - strawberry, raspberry and mango, and
- 3 spice ice creams - cinnamon, cardamom and ginger.
If each player has $1, how do you choose what three flavours to buy?
Choosing Using First Past the Post
Under a first-past-the-post voting model, you'd divide your team up into three groups of 7 and give each of them four choices. For example, one group would get to choose between vanilla, mocha, strawberry and cinnamon, another group between coconut, chocolate, raspberry and cardamom (that's the group I want to be in!), and the last between french vanilla, espresso, mango and ginger.
Since there are four choices and seven votes, it would typically take only 3 people agreeing to decide what flavour the whole groups gets. For example, suppose the votes in Group 1 were 3 for vanilla, 2 for mocha, and 1 each for strawberry and cinnamon. Vanilla would win and everyone in that group would have to eat vanilla ice cream.
Choosing Using BC-STV
Under BC-STV, all the players would be able to choose from all 12 flavours. To start, everyone would put their dollar in front of the ice cream they most wanted to buy. If any ice cream had $6 or more in front of it, it would get bought. If more than 6 players liked it, each would get some change (for example, if 8 players had each put their dollar down, they'd each get a quarter back). They could then use this quarter to contribute towards their next choice. If any ice cream was pretty unpopular (not to pick on vanilla, but really - given these other choices?) and had only one or two players wanting to buy it, the coach would tell them to move their dollar to their next choice and that ice cream would be removed from further consideration. This would continue until three litres of ice cream had been purchased. At this point, there wouldn't be enough money left to buy a fourth litre.
Interpretation: the ice cream families are like parties and the specific flavours are the candidates. The dollars are like ballots. Under BC-STV, voters have choice not only between parties, but also between candidates from the same party. In the end, almost everyone gets a flavour (candidate) they like, whereas with FPTP, you often have to put up with a flavour you don't really like just because some other people voted for it.
More Commentary
These analogies all illustrate the key ideas behind BC-STV - that voters can express their true preferences first but still have their vote count if their first choice doesn't have enough support to be elected, that different voters with different political views can each help elect a candidate they want to represent them regardless of how other people vote, and that each vote is used as fully as possible by possibly being spread across more than one candidate if one's top choice is particularly popular.
One question that's commonly asked is how many votes are needed to elect a candidate. This idea is best illustrated using the ice cream analogy. If three flavours are to be chosen ('elected'), the number of dollars ('votes') needed is found by dividing the total number of voters ($21, in this example) by one more than the number of flavours to be chosen (3+1=4, so $21/4 = $5.25) and then rounding up to the next whole number ($6). That's why we set the price at $6 in this example. This is just an extension of the common intuition that to win a majority for a single seat, a candidate needs 50%+1. For two seats, each winner needs 33.3%+1, and so on.
In a more realistic example, we might have a three seat district with 60,000 voters, so the number of votes required to be elected is 60,000 / (3+1) = 15,000, plus 1.