Re-weighted Methods Are Suboptimal

In a post I made in November 2020, I argued for a multi-winner variation of range voting called re-weighted range voting. I’ve since rescinded this view—closer analysis showed me that all re-weighted variants of range and approval voting are more vulnerable to tactical voting. I shall demonstrate this with an example. A voter loves the Plaid Party, but thinks some representatives from the Checkered Party aren’t awful. If that voter casts an honest ballot, it gets de-weighted every time a Checkered Party candidate they gave a non-zero score to wins a seat. If this voter is in a district where the last seat gets decided by a close margin, their decreased ballot weight for the Plaid Party may allow a Checkered Party candidate beat a Plaid Party candidate, especially if they didn’t give the Plaid candidate a top score. This becomes more likely when this voter doesn’t give the maximum score to a particular Plaid Party candidate. This is called vote burying and ironically hurts the Plaid Party if every voter that supports Plaid candidates did this.

Voters can vote bury in single-winner range voting, but it becomes more problematic in re-weighted range voting. In general, multi-winner voting methods designed to gather more voter information on each ballot can backfire. Voters deliberately reduce the information they give about their preferences, revealing preferences where they think their marginal impact will be greatest only. This happens because of free riding—voters in multi-winner proportional systems may choose not to vote for all the candidates they support because they expect other voters to elect them anyways.

Furthermore, the cross-party and intra-party voting variations allowed in re-weighted range make it semi-proportional only. This is bad if we want to choose voting methods that reflect voter sentiments well. In all multi-winner methods with insufficiently large electoral districts, there’s an implicit vote threshold equal to the quota of that district for any given political faction. For example, a 5-seat electoral district has a threshold of approximately 20%. This stifles smaller political factions by denying them seats. There’s a strong correlation between wasted votes and free riding with proportional representation voting methods.

Pure Proportional Systems

Party list proportional representation without an explicit vote threshold that uses D’Hondt for seat allocation is the best option if we care about minimizing wasted votes only. It’s simple too, however, it has some features many people dislike. The most glaring anti-feature for some people is lower accountability, especially on the individual level—party list elects representatives either at-large or in districts with many seats. This breaks the link between constituents and their representatives and weakens regionalism. Furthermore, party list systems using closed lists prevent constituents from having any input over candidates. Candidate Transferable Voting (CTV) is a general case of party list proportional representation that uses lists constructed by candidates in advance. I could see this system working well in small, geographically homogeneous polities but poorly in large countries with regional variation.

Biproportionality

Many people in Canada and the United States care about local, accountable representation. How can we reconcile this with proportional representation? Biproportional voting methods try to maximize both proportional representation and local representation. There aren’t any voting systems implemented now that are strongly biproportional. Mixed-Member Proportional MMP is weakly biproportional only because it the leveling and overhang seats. Both systems I discuss below work on existing voting machines and are countable in precincts.

Ranged Dual-Member Proportional

This system is like Dual-Member Proportional (DMP), but uses range voting instead of plurality voting. Here’s the steps:

1. Voters cast a range voting ballot for candidates in their districts on a 0-9 scale
   • Any candidate left blank automatically scores zero for that ballot
2. Election officials tally all the votes
3. Each political party gets 1 point for each voter who scored an affiliated candidate highest on their ballot
   • If a voter rates $n$ candidates from different parties as their co-equal favorites, the parties get 1/$n$ points from that voter
4. Election officials determine seat allocation using the D’Hondt method
5. Election officials construct party lists for each party based on what non-winning candidates had the highest average scores in their district
6. The first seat in each district gets awarded to the candidate with the highest score
7. The second seat in each district gets awarded based on the party lists election officials constructed

I think this system should use a 4% election-wide vote threshold to avoid a fractious legislature, even though it creates some wasted votes. Parties must hold range voting primaries and have the top two scoring members move to the final ballot to ensure that voters have some control over candidate selection.

PLACE

PLACE voting is a biproportional voting system designed by statistician Jameson Quinn. It tries to preserve a fairly proportional outcome while keeping single seat districts, but has a 25% district threshold and allows for voters to vote for candidates in other districts. Ironically, this system is neither fully accountable locally or highly proportional. Nevertheless, I respect what it tries to do. You can read about it here.

My Preference

Depending on the circumstances, Candidate Transferable Voting (CTV) or Ranged Dual-Member Proportional (DMP) are my favorites. I think Federal elections in the US are best off with Ranged DMP. I can support CTV for municipal elections in medium to large cities and legislative elections in small states, such as all of New England. One way to partially restore local representation is create districts with many seats for each distinct region of a state or country. Some countries using party list proportional do this, such as Belgium. This addresses concerns from rural voters and underrepresented regions by ensuring that there’s more geographic fairness. The seats per districts must be no fewer than 15 to keep wasted votes low. Despite the differences between these two systems, I’d be elated to participate in an election with either.