Monday, September 7, 2015

Just Say No to "None of the Above"

A graphic showing an example ballot line to vote for none of the above.
Some OpaVote users use a "None of the Above" (NOTA) option when voting to fill an office.  Others call this a "Seek Further Candidates" (SFC) option, a "Reopen Nominations" (RON) option, or an "All Candidates Suck" (ACS) option.  The reason for a NOTA/SFC/RON/ACS option (hereinafter "NOTA") is to allow the voters to decide that none of the candidates are worthy of being elected and that the organization is better off leaving the position vacant for the present time.

In my opinion, organizations are better off not using a NOTA option.  I'll explain my reasoning here. But if you insist on using a NOTA option, you need to make sure you do so correctly and I'll also explain how to do that.

If you disagree, feel free to let us know in the comments or send me an email.  I can post your views in a follow up post.

NOTA is Too Negative

By including a NOTA option on the ballot, an organization is making the statement that it is possible that all of the candidates running for the position are so unqualified that the organization is better off leaving the position vacant.  That is a harsh statement.  Organizations generally include people who are more or less like minded on some issue so their elections should be much less divisive than say the election for president of the United States.  If an organization feels that NOTA is a necessary option for its elections, then perhaps it needs to reevaluate how it operates and work to improve itself.

There are better choices than using a NOTA option.  Instead, the organization could work harder to make sure that it is actively recruiting good people to run for offices.  If there are elections where only one person is on the ballot, perhaps there are too many offices, and the organization would be better off with fewer offices.  If the organization has divisive factions, then learning to understand each other and work together would go a long way to help the organization be more productive.

If, despite my objections, you still want to use a NOTA option, then continue reading to make sure you do it the right way.

The Right Way to Implement NOTA

If you do want a NOTA option, it is easy to do so with ranked voting, and you don't need to add an explicit NOTA candidate to the ballot.  How this works is slightly different for electing a single person (e.g., with IRV) and electing a group of people (e.g., with STV) so I'll explain each separately.

As an initial matter, to implement NOTA in any election (either for a single person or for a group of people), the voters must have the option to rank some but not all of the candidates.  By not ranking a candidate on his or her ballot, the voter is declaring that the voter would prefer to leave the office vacant rather than elect that candidate.  It is very important that you inform voters of this as a voter may otherwise only rank his or her top two or three candidates not realizing the implication of leaving candidates off the ballot.

NOTA for Electing a Single Person

Suppose that candidates are competing to fill an office and IRV (I'm assuming you know how IRV works) is being used to count the votes.  Each voter has the option to rank all the candidates, some of the candidates, or none of the candidates.

When a voter ranks fewer than all of the candidates, it is possible that all the candidates ranked on the ballot are eliminated, and in this case, the ballot is said to be "exhausted."  The simplest example is where the voter ranks only candidate, and that candidate is eliminated.

After concluding an IRV count, there will be a single candidate with the largest number of votes.  An organization has two options for its election rules (presumably specified in advance): (i) the candidate with the largest number of votes is elected regardless of the number of votes received (no NOTA option), or (ii) the candidate with the largest number of votes must be ranked on at least a majority of the ballots to be elected and otherwise the office remains vacant (the NOTA option).

IRV counts are often terminated either when a candidate reaches a majority of the votes or when only two candidates remain.  When implementing NOTA, you may need to go further and eliminate the second to last candidate as well.  For example, suppose there are 100 voters and when only two candidates remain, candidate A has 40 votes, candidate B has 30 votes, and 30 votes have been exhausted.  Candidate A has not yet reached a majority, but that does not mean that A is not elected.  We now need to eliminate candidate B and transfer those votes.  Any vote for candidate B that has a ranking for A will now get transferred to candidate A.  After doing so, candidate A is elected if A has reached a majority.  If not, the office remains vacant.

The principle is similar for Condorcet and approval voting.  A candidate is elected as long as that candidate is ranked on a majority of ballots or has been approved on a majority of ballots.

NOTA for Electing a Group of People

The principle is similar when electing a group of candidates, but it is a little more complicated.

Suppose that candidates are competing to fill N seats on a committee or council and STV (I'm again assuming you understand how STV works) is being used to count the votes.  When counting votes with STV, a winning threshold or a quota is used to determine whether candidates are elected.  The winning threshold is almost always a variation of the Droop quota.

After concluding an STV count to fill N seats, only N candidates will remain in the count as the other candidates will have been eliminated.  The organization again has two options for its election rules: (i) the N candidates with the largest number of votes are elected regardless of the number of votes received (no NOTA option), or (ii) only candidates who have received at least a winning threshold of votes are elected and if fewer than N candidates reach the winning threshold then some of the seats remain vacant (the NOTA option).

There is one more twist for implementing NOTA with STV.  The winning threshold for STV can be "static" or dynamic," but to implement NOTA you must use a static threshold. A static threshold is calculated before the votes are counted and does not change.  This is exactly what you want when using NOTA.

A dynamic threshold is recalculated every round based on the number of exhausted ballots.  At each round, the number of unexhausted ballots (as opposed to the total number of ballots) is used to compute the threshold.  Because the number of exhausted ballots can increase each round, the dynamic threshold can decrease each round.  In fact, the whole point of the dynamic threshold is to ensure that all winning candidates do reach the winning threshold by reducing the threshold as the number of exhausted ballots increases.  Implementing NOTA and using a dynamic threshold are directly counter to one another.

Now that you know how to properly implement NOTA, let me explain a common incorrect way of doing it.

Do Not Put a NOTA Candidate on the Ballot

Some organizations want to explicitly put a NOTA candidate on the ballot.  In my view, this unnecessarily complicates the election and does not provide any benefits.  Here are some reasons.

First, as described above, one can achieve the goals of NOTA without explicitly putting a NOTA candidate on the ballot so there is no need to have a NOTA candidate.

Second, if you do have a NOTA candidate, the NOTA candidate must always be ranked last on the ballot.  This complicates the user interface for electronic voting and invites voter errors for paper voting.  Note that OpaVote does not currently support a NOTA candidate that is always ranked last.

Third, and most importantly, using a NOTA candidate greatly complicates the counting rules because the NOTA candidate is treated differently from other candidates (this is especially true for STV).  I have never seen counting rules that properly describe how votes should be counted when there is a NOTA candidate.  If you know of such rules, please send them to me.  I'll sketch out how I think it could work with IRV and STV.

When you have a NOTA candidate, you need to distinguish between (i) a ballot that ranks a candidate first and ranks the NOTA candidate second and (ii) a ballot that ranks a candidate first and does not rank any other candidates.  In aggregate, we have ballots that support candidates (the ranked candidates),  ballots that explicitly reject candidates (when NOTA is on the ballot), and ballots that take no opinion on candidates (when NOTA is not on the ballot).  This gets confusing very quickly!

As a thought experiment, let's think how one could implement a NOTA candidate with IRV.  The NOTA candidate can't be eliminated.  At each round, the real candidate with the fewest votes is eliminated until only one candidate is left.  If that one candidate has more votes than the NOTA candidate, then that candidate wins.  (That wasn't too bad, but I still believe it is better to not use a NOTA candidate.)

Now let's consider how one could implement a NOTA candidate with STV.  The NOTA candidate can't be eliminated, and I suppose the NOTA candidate also never transfers surplus votes.  

First, let's consider STV with a static winning threshold. As the count progresses, the NOTA candidate will accumulate votes and ballots will be exhausted.  The NOTA candidate can receive more than a winning threshold of votes and any number of ballots may be exhausted.  At the end of the count, how do we determine who the winners are?  We can't require that winning candidates have more votes than the NOTA candidate (as we did above for IRV), because if the NOTA candidate has more than a winning threshold, then no one is elected and all seats are vacant.  That does not seem to be the intent of using a NOTA candidate.  The only thing that makes sense is to require that candidates receive at least a winning threshold of votes to be elected, and thus we are in exactly the same situation as if we did not use a NOTA candidate at all, and we have added all this complexity for nothing.

Second, let's consider STV with a dynamic winning threshold.  Under a normal STV count with a dynamic threshold, the winning threshold is determined by using the number of unexhausted ballots, and thus the winning threshold decreases as the number of exhausted ballots increases.  Now, it is possible to distinguish ballots that rank the NOTA candidate and ballots that do not.  We simply compute the dynamic threshold the same way.  When a ballot is exhausted the winning threshold will decrease, and when a ballot reaches the NOTA candidate, the winning threshold will not decrease because the ballot is not exhausted.  At the end of the count, candidates who reach the dynamic winning threshold are elected.  While this could be done, in my view, it is far too complicated, and you should just say not to using a NOTA candidate with STV.

In summary, I think it is a bad idea to use a NOTA candidate with IRV and it is a terrible idea to use a NOTA candidate with STV.

Although OpaVote does not officially support counting with a NOTA candidate, it may work for you anyway for an IRV election.  As long as the NOTA candidate is not eliminated, the results should reflect a correct implementation of a NOTA candidate.  If you do this, you should closely review the round-by-round election results to make sure the outcome is what you intend.  If it doesn't, then you need to fall back to a hand count.

So that is my tirade.  I suspect people out there will have other views and I would love to hear them.