Quadratic Voting: One Man, 100 Votes
What if we gave people 100 votes instead of one? To what extent should we pursue institutional reform rather than focusing on policy to bring about our priorities?
This is Part 1 of a series in the Rules of the Game that will focus on the tensions between optimal policymaking and traditional institutions within a democracy.
It would seem that in a world where a child’s life can be saved for $2,300 (a relative pittance), focussing on the rules of the game directly might be a less impactful area of research/resources. Perhaps I should be working a second job and donating the proceeds to save more lives instead of writing this blog?
Nonetheless, using one’s comparative advantage in research is also a good way of maximising your impact. And so, instead of rehashing the debates over more popular alternative systems such as Proportional Representation or Alternative Vote, I am going to give my thoughts on a niche electoral system - Quadratic Voting.
This post will attempt to (1) ascertain the key features Quadratic Voting, (2) analyse its implications, and (3) evaluate the extent to which it effects traditional notions of democracy. It also contains a lot more questions than usual - I am trying to find answers to help me with other research.
What is Quadratic Voting (QV)?
QV allows voters in an election to assign multiple votes to an issue or candidate of their choice at a quadratic cost.
Quadratic, how? Because the Quadratic Votes (QVs) which are assigned are converted to Actual Votes (AVs) to be counted according to their square root. Stay with me…
1 QV will apportion 1 AV. 4 QVs will apportion 2 AVs. 9 QVs will apportion 3 AVs. And if you are good at your mental maths you will already have figured out that… 16 QVs will convert to 4 AVs. 25 QVs will give 5 AVs… And finally, 100 QVs will apportion 10 AVs.
Instead of using 1 vote on a single election or referendum every few years or so, as is usual, you can spend a part or all of your 100 votes several times a year. If this makes no sense, perhaps TABLE 1 will.
The marginal cost of each extra vote is more than the last. In other words - each vote is more expensive than the last by a proportionally larger amount each time.
A simple ‘plurality’ voting system, like the one used in UK General elections, allows voters to express only their binary decision: ‘Yes’ or ‘No’, or ‘Candidate A’ or ‘Candidate B’. QV tells us this same information whilst also simultaneously expressing how intense the preferences are for one side or the other.
If voters assign more QVs to one issue/candidate they have relatively more intense preferences for, a minority of individuals can actually win an election against a larger minority. This is a key feature of QV as a voting system: it would allow a minority of voters with intense preferences to win an election. Something that incumbent plurality voting systems (such as the UK’s First Past the Post) do not allow for.
Why is it important that the intensity of preferences are acknowledged by a voting system? Because some argue that tyranny of the majority plagues most Western voting systems - which means that majority’s almost always win in elections.
Minority views - which could constitute 49.99% of the voting population - are routinely dismissed at the expense of the wants of the majority. The majority wants could be indifferent though, and the aggregated strength of their preferences much lower than the minority bloc. Is this fair? I think technically, yes. But intuitively, no.
Imagine this…
That a country has 5 Policy Votes a year, on policies we might like or not like to vote for. Only 1 Policy can pass. The policy options might be as follows:
Banning the export of cheese.
Extending the vote to 16-year-olds.
A basic income of £1,000 a month.
Pedestrianisation of all streets.
To triple funding into synthetic wombs.
A voter is given 100 QVs (let’s say) to apportion them how they like. Subject to the quadratic cost we covered in the previous section.
I might be a huge fan of Policy 3 (a basic income), and give my whole 10 votes (which would cost 100 QVs) to that policy. Or I might split 5 votes (25 QVs) across 4 of the policies and leave one out.
This means even if less actual citizens voted for a policy like number 3., they could win the election still. 6 citizens giving 100 QVs each (600 QVs) would beat 20 citizens apportioning 25 QVs each (500 QVs). 6 citizens can win an election over 20 citizens.
But QV does not have to be used for a multiple-choice referenda such as this. It can also be used on a more local scale to reveal citizen intensity of preferences.
Take this fictional example…
Imagine that a council has brought forward a vote on the issue of whether to fund the building of a new, waterproof bus station. A large minority of the community with relatively intense preferences would greatly benefit from this as they use public transport a lot, because it often rains and the old bus station leaked.
A slim majority does not have strong views about the new bus station, but in sum does not want to allocate cash to it. In a plurality system, this would mean that the majority can block the bus station at the expense of the impassioned minority, even though when preferences are aggregated the community overall loses out from voting against the proposal.
If the minority bloc is constituted by 25,000 people who would vote for and value the project at £100 each, and the majority bloc constituted is by 30,000 people who would vote against and disvalue the project at -£35 each, the majority wins: the bus station will not be built.
Even though the new bus stop would have generated £1.45m (£2.5m minus £1.05m) of net social utility, this more efficient situation is never realised. FPTP seems to not only quell the wants of a large minority bloc with strong preferences, but also lower net social utility and make people relatively worse off because of the vote.
Would QV always ensure minority wins? No - because the minority bloc must still be large enough and hold relatively intense preferences to defeat a majority, and if the majority is only moderately impassioned, the majority will win most of the time. QV might, however, increase the likelihood that vociferous minority blocs win more often…
A real example…
‘In the Spring of 2019, the Colorado State House of Representatives’ Democratic Caucus implemented a QV system to ascertain which policies had the most vociferous net support among them. Each of the 41 caucus members were given 100 QVs to pick their favoured policy among many, which turned out to be the ‘Equal Pay for Equal Work Act’, which received 3,600 QVs and was introduced as law in January of 2020.
Here, QV helped to facilitate the vote outcomes that are most likely to ‘maximize the sum of [their] utilities’ (Goeree, Louis and Zhang, 2020: 2), rather than just increasing the utility of the winning bloc, as a plurality voting system does.
Could QV be good or bad for Democracy?
I define democracy as a system of governance whereby those who rule are elected by enfranchised citizens. I will suppose that a democracy is more democratic when a) more citizens are enfranchised, b) citizens views are usually enacted upon, and c) that there is some method of removing those in power.
Is QV less democratic because it increases the likelihood of more minority wins? Which in turn will increase the likelihood that the ‘democratic’ majority’s views are not acted upon.
Or is QV actually more democratic because it shares and spreads election wins away from majorities who win most the time to minorities who may get a couple wins per cycle?
Where should the trade-off sit? Is it okay to dilute democracy to bing about desired ends? Should we make weaker our traditional majoritarian systems to quell poverty and child mortality abroad? Perhaps lives saved > the extent to which a government is democratic?
Should we lessen the say those have now to protect the lives of those who will live in the future?
Is the logical extension of a Longtermist democracy (meaning one interested in safeguarding the lives and reducing the suffering of those beings yet to be born) that we should forego/at the very least give much less weight to the democratic wants of those citizens alive now, because they will be outnumbered by a quadrillion future humans?
This is slightly off topic… but will take up much of my further blogposts.
Conclusions
I think that QV could help in more localised and decentralised decision-making settings. In local councils, in governing bodies, perhaps shareholder meetings, etc. I am not sure how politically palatable QV would be if used in the UK to choose policy.
As Brexit seemed to highlight, there is a view in the UK that a majority’s say should be final. I think introducing QV would be troublesome and the positive effects of more likely minority wins would potentially be outweighed by a negative aesthetic and substantive view of these minority wins as undemocratic. That the majority wins is viewed as a strong British democratic tradition.
But is this a slippery slope? If we found that actually making a traditional democracy weaker gave us more effective results with regards to our priorities, how should we act upon that information? A fictional benevolent dictatorial being with perfect knowledge might solve the world’s ills but is that worth the disenfranchising of the citizens? I don’t think so.
This is a massive straw-man of EA and Longtermist beliefs (which I don’t hold). But I am just trying to see where the arguments go… Thanks for reading! Next time I’ll look at how institutional reform can bring about Longtermist priorities.
Email any thoughts (anything you liked/comments/tips?) to:
connor.axiotes@googlemail.com