This is the second in a series of articles looking at STV data from the OpenStreetMap Foundation Annual General Meeting ballot measures. In this article I look at vote rank and the number of votes per ballot and how that relates to different candidates.

## Candidate ranks on ballots

Let's take a look at the rank of candidates listed on the ballots.

[This graph has been updated. The data was incorrect in the first version as I made an error in collecting the data. Sorry. The text below has been adapted as well, because, well, the text relates to the graphs.]

From this view it is tempting to say, Well look at all of those first rank mentions,

and presume that Frederik, Steve, and Kathleen will fill the three available seats. Looking further at the second rank votes we see Kathleen, Frederik and Paul assembled for the first time.

One of the other election scrutineers, Ilya, has some more analysis of candidate rank in this diary entry.

While the first rank count doesn't tell the whole story of the election, niether does the last rank. My naive expectations were that winners

would have more first rank mentions and fewer last rank mentions. That was not the case in the OSMF 2014 election as seen above.

Two of the eventual winning candidates, Kathleen and Paul are least-mentioned in the eighth rank, along with Peter and Marek. While Frederik, the first rank favourite is also a popular last-rank candidate.

It appears that STV is more complex than my naive expectations.

[Thank you, Zverik for pointing out my graph error so that I could correct this section.]

## Number of votes per ballot

We looked earlier at the number of votes on each voter ballot and found that the election incuded a blank ballot with 0 candidates, and ballots of every permitted size from one to eight candidates. Most common were the full slate ballot where all eight candidates were listed. Full slate ballots comprised roughly one third of all ballots cast.

I decided to put that on a graph. It is the worst graph ever.

When there are eight candidates and eight places on the ballot, guess what? Every candidate gets an equal number of mentions on the full slate ballot. Not the most-compelling graphic. I'll save you the pixels.

### Hypothetical result: Full slate ballots only

Oddly, if I run the same election and use only the full slate ballots, the same three candidates are elected. Other mechanics of the election are changed; the threshold is lower and the election takes seven rounds rather than eight. So I guess that is another difference between STV and first past the post. The rank on the ballot really matters.

As a caution, this is completely hypothetical and has no impact on reality. I'm just playing with numbers and STV.

## Candidates and ballot length

The ballot length data is more interesting where the candidates differ. So I dropped the column for ballots with eight candidates listed, and graphed the rest. I've called the number of candidates on a ballot, the ballot length.

The shape mimics the mentions

graph from the ealrier article in this series, and it should. I've hidden the ~80 ballots in which every candidate is mentioned. So this might be considered the more varied and more interesting top

of that graph. What jumps out from that graph?

For me, it's the variation around candidate results on three-vote ballots. Let's take a look at those.

## Next most common: the three-vote ballots only

With fifty-six ballots or about one quarter of the full election, the three-vote ballot is second most-common. This graph presents a different shape than the others.

One of the candidates elected in the real election is in the bottom half of candidates in this graph. Granted, this graph of mentions

ignores rank position and we have seen in the examples above that rank has its privileges. What happens if we run just the three-vote ballots through a test election?

[Sorry to interrupt again. Zverik pointed out an error in this graph as well. I've corrected it and updated the text. Now, back to a Very Special Episode of Stat blast 2.]

### Hypothetical result: Three-vote ballots

So I tried that. I was not surprised that the results were different, but I was surprised that they differed so little.

In the hypothetical election where only the ballots with exactly three votes are counted, the winners were, Frederik Ramm, Kathleen Danielson, and Steve Coast.

So two candidates from the lower half of the graph when considering mentions, are elected when considering the positional rank of those mentions. Neat stuff.

## Next

So we've seen that number of votes alone, or mentions

don't tell the whole story. And we've seen that vote rank, alone doesn't tell the whole story.

So what tells the whole story? I don't know yet. But I'm having fun along the way.

Next time, let's look at combinations of candidates.

Your feedback in the comments, by e-mail or on social media are welcome.

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