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The finer details of Meek's STV

Submitted by: @import:stackexchange-cs··
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thestvmeekdetailsfiner

Problem

Meek's version of the Single Transferable Vote system [.pdf] is used in multiple big elections including those of New Zealand and Stack Exchange.

Demonstration (with thanks to the Department of Internal Affairs of New Zealand).

I have a basic understanding of how the votes are counted, but there's one thing I haven't been able to figure out.

What happens if positions are left blank?

For example:
Assume 6 candidates and no limit on the amount of choices.

One could vote (where left is first vote and right is last): 3 4 5 6 1 2 or 4 5 6 and leave the rest blank.

In the STV system, the following is legal as well: 0 2 4 0 1 6
What would happen in that case?

Will the choices be shifted to clear it from any left-open positions or will the votes be counted at the moment indicated by the position? Those options will (likely) influence the election both in different ways.

I'm not a CS expert in any way, just trying to get the hang of an interesting system to implement my own vote counter.

Solution

In Meek STV, there is the concept of the quota or threshold that a candidate must exceed to be considered elected. This threshold is changed from round to round in the Meek STV system. The threshold changes based on how many votes are thrown away.

Let's say that your code is 4 5 6 and the rest blank, then once all those candidates are either elected or eliminated, the remaining part of your vote is considered "thrown away". Based on this, the threshold is changed for what candidates need to be elected in the next round.

In the STV system, the vote 0 2 4 0 1 6 is considered the same as 2 4 1 6 0 0, i.e. the zeros are automatically put at the end.

In the Stack Exchange moderator elections, it is possible to choose only a second candidate and a third candidate, but not a first. That is the same thing as choosing a first candidate and a second candidate.

Related on Meta Stack Exchange: How are moderator election votes counted, in pure English?

Context

StackExchange Computer Science Q#48149, answer score: 2

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