A brief survey of ballot types

There are two sides to voting systems: ballots and aggregate functions. Ballots describe individual voter preferences, whereas the aggregate functions convert batches of preferences into winning candidates. Having already discussed properties of the aggregate functions, let’s take a look at ballot types.

Checkmark ballots

	Mark one
Candidate A
Candidate B
Candidate C
Candidate D	X
Candidate E

If you’re from North America, this ballot type should look quite familiar. Voters express a preference for a single candidate. The ballot contains little information (in that no addition preferences are expressed), but it’s dead simple. It’s most frequently used in conjunction with plurality voting.

Checkmark ballot variants

	Mark any
Candidate A	X
Candidate B
Candidate C	X
Candidate D	X
Candidate E

Some variations on checkmark ballots exist, the most notable of which permits voters to select multiple candidates (see approval voting). While this increases the contained information, it does so at the cost of simplicity.

Preferential ballots

	Order
Candidate A	3
Candidate B	4
Candidate C	2
Candidate D	1
Candidate E	5

Instead of selecting candidates, preferential ballots ask voters to order the presented candidates from most to least favoured. More information is contained than vanilla checkmark ballots, but with the added burden of requiring voters to order all candidates. This type of ballot is used by instant-runoff voting.

Preferential ballot variants

	Order
Candidate A	2
Candidate B
Candidate C	1
Candidate D	1
Candidate E

Variants can address a number of the problems with preferential ballots. In the given example, note that the voter hasn’t ranked all candidates. Also note that the voter has ranked both Candidates C and D in first place. These two modifications increase the contained information while decreasing the complexity. Ballots that allow ties and unranked candidates require more aggregate functions, such as Ranked Pairs or the Schulze method.

Rating ballots

	Rank (-5 to +5)
Candidate A	0
Candidate B	-3
Candidate C	+5
Candidate D	+5
Candidate E	-5

In rating ballots, voters express preferences for each candidate independent of the others. Most notably, this ballot type includes magnitude of approval and, consequently, more information than any of the previously discussed types. While it’s certainly more complex than checkmark ballots, one could argue that it’s simpler than preferential ballots (doesn’t require strict ordering). This ballot type is most commonly associated with range voting.

Rating ballot variants

	Rank (0 to 3)
Candidate A	1
Candidate B
Candidate C	3
Candidate D	3
Candidate E

Variants modify the granularity of magnitude and the value assigned to unranked candidates. The given example is simpler than vanilla rating ballots, but contains the same information. The voter has expressed a strong preference for Candidates C and D, while at the same time expressing a weak preference for Candidate A.

Ballot conversions

We can map some ballot types onto others if our aggregate functions require it. For example, I very much like Ranked Pairs’ aggregate function. It’s reasonably simple and produces fair results that pass a large set of voting criteria. The down side is that it requires preferential ballots, when I prefer rating ballots. Let’s convert a rating ballot into a preferential ballot.

The end lesson here is that we can simplify our ballots without compromising too much on information density. I have the feeling that more people would be okay with rating each candidate than with explicitly specifying an order.