In countries using Single Transferable Vote, how are voting results presented?

Question

In electoral systems based on parties, it is easy to publish the results: it is sufficient to publish the number of votes each party received. These numbers contain all the information that is needed to compute the election outcome.

But in single transferable vote, each voter votes by ranking the candidates. The potential number of different votes is the factorial of the number of candidates, which may be enormous. It may be impossible to publish all these results.

Is there an efficient way to publish the results of STV elections, such that the published information can be used by observers to compute the election outcome?

Answer 1

Let's consider the classic example: Australia, which has used STV/IRV for more than a century.

For calculations of votes, we need to consider each electorate separately. Calculation of the global outcome (seats won etc.) is trivial.

It should be noted that in any voting system, tallying the final result given "the number of votes each party received" is a technical process and is rarely controversial. The process is more complicated for STV, but it's still pure math. Controversy may arise at the earlier stages: how exactly ballots are counted, what is considered informal (invalid) vote, how ballots are presented, etc. This is where most scrutiny is needed.

Generally, for the public, the results are presented already calculated and ranked. They still present the "number of votes" for each candidate, but this number is calculated in a less trivial manner than just adding up votes. Still, the process of calculation is also presented for those who are interested.

Here is an example from the most recent federal elections for the electorate of Adelaide. (This is the lower house election, which is IRV - a single winner version of STV. It is a bit easier to demonstrate, but the principle is the same. Note that Senate is still elected by candidates, not parties; just there are multiple winners in the last round and the threshold is lower than 50%).

The (abbreviated) "final" table looks rather "normal":

Candidate	Votes	%
GRANTHAM, Amy	42,948	38.09
GEORGANAS, Steve	69,816	61.91

The catch is that there are only two candidates shown out of 7! This is because other candidates were eliminated in the STV counting process, and their votes were redistributed to these candidates. This is essentially the result of the last round of counting. In Australia, this is often called Two party preferred or Two candidate preferred result.

Next thing presented (and often publicised) is the First preference count for each candidate. This is the exact number of ballots which gave first preference ("1") to this candidate, like if it were "traditional" elections. We can see that for these two candidates, the count is different and much lower:

Candidate	Votes	%
GRANTHAM, Amy	36,080	32.00
GEORGANAS, Steve	45,086	39.98

In STV, this first preference count has largely psychological/symbolic value. In this example, we can see that a third of votes for the ultimate winner Steve came from other parties, whereas Amy had much higher share of "personal" votes. Of course, it is a well-known feature of STV that the final winner may not be the one who had the most first-preference votes.

Nevertheless, there is an "implementation detail" in Australia that parties/candidates who get enough first-preference votes (a fairly small percentage) get certain monetary compensation for the election expenses. This is to avoid a flood of spurious candidates who might register just "for fun".

The next thing one may wish to examine is the Full distribution of preferences table on the same page. There, each round of counting is presented, starting from first preference and culminating in the two candidate preferred result. It is clearly observable how, for example, the 870 votes from the first-eliminated candidate are distributed to the remaining 6 candidates in the second round, and so on.

Here, by the way, is where Senate election with its multi-winner count gets more complicated. There, if a candidate gets more votes than the quota requires (at any round), the "excess" votes are taken away and redistributed to other candidates with the proportional weight. As a result, each elected candidate gets exactly the same number of votes in the final round, and everyone else gets 0! This is not required for IRV as such process will not change the ultimate winner. The calculation is also published, but it is a multi-page PDF document (example of a smaller one for Tasmania - 30 pages).

For those who want to scrutinise further, AEC publishes the results in machine-readable formats as well.

Answer 2

Adding on further context to Zeus's very good answer:

In Australia, where the Senate results are done using STV on a per-state level, voters are allowed to vote for a party as a whole, rather than being required to vote for each candidate individually. This is called "above-the-line" voting. The vast majority of voters choose this path, though the option still exists to number each candidate individually ("below-the-line").

The headline figure seen most often is the number of first preference votes cast above-the-line, or the sum of the party's above-the-line votes and the votes given to each candidate below-the-line. See this page for the Queensland results of the last election for an example.

In reality, to make them more consumable, these raw vote counts/percentages are often converted into "quotas", representing the fractions of a seat that have been won by that party.

Group	Candidate	Party	Votes	%	Quotas
J	Above-the-line Votes	Queensland Greens	345,470	11.46	0.8024
	ALLMAN-PAYNE, Penny	Queensland Greens	21,671	0.72	0.0503
	SRI, Anna	Queensland Greens	1,718	0.06	0.0040
	Group Total	Queensland Greens	373,460	12.39	0.8674
S	Above-the-line Votes	Liberal National Party of Queensland	1,013,227	33.62	2.3533
	McGRATH, James	Liberal National Party of Queensland	21,411	0.71	0.0497
	CANAVAN, Matt	Liberal National Party of Queensland	11,822	0.39	0.0275
	STOKER, Amanda	Liberal National Party of Queensland	11,981	0.40	0.0278
	Group Total	Liberal National Party of Queensland	1,061,638	35.23	2.4658
Y	Above-the-line Votes	Australian Labor Party	713,051	23.66	1.6561
	WATT, Murray	Australian Labor Party	21,847	0.72	0.0507
	CHISHOLM, Anthony	Australian Labor Party	2,183	0.07	0.0051
	Group Total	Australian Labor Party	744,212	24.69	1.7285

Note that the "group total" counts are indicative only, and not of any formal value in the ballot count.

From this table you can see that Penny Allman-Payne received 0.85 quotas on first preferences (above the line group J votes give first preference to her), meaning she needs to receive 0.15 more quotas in subsequent round to get elected. James McGrath received 2.4, so he passes 1.4 quotas down to second preferences, at least 1.35 of which will definitely go to Matt Canavan (because above-the-line group S votes give second preference to Canavan). So Canavan receives at least 1.37, and passes at least 0.35 to Amanda Stoker, who therefore is guaranteed at least 0.37 quotas.

For most people, this high-level count is sufficient. Guesses at how many total quotas a candidate will receive can be made by an understanding of party preferences. For example, "Animal Justice Party" above-the-line voters are likely to preference the Greens, while "One Nation" voters probably preference the LNP. So Greens' total quotas can be estimated by adding their own first preference vote to the vote of AJP, as long as you assume AJP candidates will not win a seat, and their voters will not preference a different party which does win a seat first.

For those who want to fully validate the election results, a full list of every formal vote is published. So is a summary of the distributions of preferences at each round of the count. You can see the links to these for the 2022 election here. You can also get counts of things like how many votes were informal (often referred to as "spoilt" ballots, i.e. ballots which were not filled out in a way that allows them to be counted).

Answer 3

In the case of New York City's latest mayoral primary the data was made available in the form of a collection of CSV files (click on 'Download CVR data'). There's no metadata or readme accompanying it, but Alec Barrett has published an 'unofficial' readme on GitHub. This data was previously used on Politics.SE to calculate the Condorcet winner of that primary.

I suspect that the same method of releasing data is used in all jurisdictions where STV is used.