Collective Decision Making

Lesson highlights

Decision
making systems

Common systems
Goals and trade-offs

Voting mechanisms

Common mechanisms
Desirable criteria

Collective decision making

An umbrella term that contains voting mechanisms,
governance processes, policy making, budget allocation.

Collective decision making

A way to gather the opinions of a heterogenous collective.
A way to aggregate their preferences in a concise way.
A way to reach a decision over the definition, resources, privilege or authority of a collective.

Why?

A prerequisite for the formation of countries, companies, dynasties, i.e., strong institutions.
Agile decision making helps collective react to external changes: war, trade, migration.
Internally, they enable stability and progress: money, laws, private property.

Why?

Even high tech, highly automated projects remain human collectives at their core.
A project's decision-making mechanisms ensure its strength and relevance over time.
We should consider these mechanisms along with the project's economics and security.

A more profound interpretation

Long you live and high you fly
Smiles you'll give and tears you'll cry
And all you touch and all you see
Is all your life will ever be

-- Pink Floyd (Breathe)

Any single entity may be identified as the aggregate of its (inter-)actions with its external environment. If a system's governance wholly defines these, it may properly be considered to identify the entity.

Common systems

Dictator, unelected or elected.
Unelected committee (Zurich guilds).
Representative democracy -- elected committee.
Political parties
Direct democracy -- all participate in all decisions.

Goals


Utility	- decision maximizes society's welfare - it reflects people's preferences
Legitimacy	- decision is considered fair - people trust the process
Practicality	- process is fast - it is simple to understand

Goals

A dictator is practical. Is it legitimate?
Direct democracy is legitimate. Why not always use this?
Which mechanism maximizes utility?
Which is best in case of war?

Dictator

Legitimate?
It is very practical.
Good in case of an emergency.
Only stable as long as the individual is stable (unlikely to be forever!).

What's wrong with a dictator? We typically think of it as illegitimate, but keep in mind that kings used to be considered legitimate in the past. And even today, the owner of a large tech company may be able to make unilateral decisions that impact millions of lives, and we consider this to be legitimate.
It is practical and allows for fast decision making in case of an emergency. For example, in the next pandemic, would you like to have every city vote on whether and when face masks should be mandatory in public spaces? Or would you prefer to have an authority impose it?
You could also argue that it leads to stability, as people can expect things to stay the way they are for the foreseeable future, and can plan accordingly. However, we also have several real-life examples where a dictator behaves erratically.

Democracy

Simple Direct Democracy

Every person is consulted on every decision.
Considered highly legitimate.
Good at revealing the collective's opinions.
Leads to progress as anyone can propose ideas.

Simple Direct democracy

Compare to a two-party system

For instance, imagine a two-party system like the US where people are forced to pick one of two parties, instead of directly casting their vote on every decision. Imagine the left party traditionally supports legalizing abortion and banning firearms, while the right party traditionally supports banning abortion and legalizing firearms. Such idiosyncrasy could have made sense in the past, but if there is a shift in preferences whereby more and more people want to legalize both abortions and guns, the system will not have the means to detect these preferences and adapt properly.
Similarly, if neither the left party nor the right party supports universal healthcare, then people who support healthcare do not have a voice.
Of course, similar issues remain for a multi-party system (more than two political parties), and the issues are even worse in a dictatorship.

Simple Direct democracy

Not very practical:
asking everyone to vote.
One decision at a time.
Not great for emergencies.

Voting paradox

Does direct democracy maximize utility? Probably not.

Example: Option A: 0 dollars Option B: 100 dollars

Prob. that my vote flips the result from A to B: <0.1%.

So, my expected profit for voting is <10 cents.

We saw that direct democracy is legitimate but not practical. How does it fare in terms of utility? Relatively well, but we argue here that it is not ideal, due to something called the voting paradox.
Suppose the collective must decide between options A and B, and I personally value option A as worth zero and option B as worth $100 to me.
Now, if most people vote for A, then A wins even if I vote for B, and if most people vote for B, then B wins even if I don't vote at all. Hence the most likely event is that my vote does not change the outcome.
When the number of voters is in the millions, the likelihood that my vote actually changes the outcome is tiny, well below $0.1%$ . My expected profit for voting is then (my profit for B - myr profit for A) $\times$ prob. that my vote flips the result.
In this example, my expected profit is less than 10 cents, which probably does not justify the effort of voting.

Voting paradox

Voting paradox: For a rational, self-interested voter, voting costs will normally exceed the expected benefits.

Minimal chance that single vote changes collective decision, so most of the time the individual voting benefit is zero.

A common good game: globally optimal if everyone votes, but personally optimal not to vote.

Voting paradox

Voting paradox: For a rational, self-interested voter, voting costs will normally exceed the expected benefits.

It leads to a low turnout, which affects legitimacy.

Turnout: percentage of people who choose to vote.

Rational ignorance

Rational ignorance: refraining from learning when the cost of educating oneself on an issue exceeds the expected potential benefit.

As a result, most people will not vote judiciously.

Rational ignorance

Whether or not someone votes can be biasable.

40% of the population supports a new proposal, while 60% rejects it. However, a company who will profit from the decision lobbies for the 'aye'. 50% of supporters and 30% of detractors vote. As a result, the proposal passes.

Solutions to the voting paradox

Representative democracy: elect a committee, whose members represent well the preferences of the passive people.
Delegated voting: give your voting power to a person who understands the issue well, so you don't have to.

Advanced Forms of Democracy

Liquid democracy/delegation
OpenGov/multi-track delegation
Quadratic "replacement" voting
OpenGov/Optimistic approval
...

Solutions to the voting paradox

Both solutions based on desire of representing every clique in the collective.
Delegated voting is organic, helps with turnout, but remains slow.
A committee ignores preferences of small cliques, but can take complex decisions fast.

However, people naturally tend to congregate with other people with similar preferences, to form what we call cliques. So, you tend to be well represented by voters in your clique. The idea of both systems is to "sample" some opinions for every clique.
From my point of view, delegated voting remains very close in spirit to direct democracy, as every individual remains free to vote directly if they choose to do so, or they can choose a representative that represents them very well. We gain in terms of practicality as now fewer people need to vote, but the process is still slow and can only take binary decisions.
On the other hand, a committee is a bit closer to a dictator. It does a good job at representing the most common preferences of the collective, but not the preferences of small cliques. On the other hand, it can make subtle, non-binary decisions, and can make them fast.
Hence, it could be a good idea to use delegated voting for important, binary decisions (such as whether to make abortions legal), and an elected committee to make emergency decisions (such as what to do in case of war). I encourage you to consider how you would design an ideal decision making system.

System capture

Does a dictatorship maximize utility? Also probably not.

System capture: A decision-making system in which a clique manages to impose its opinion consistently.

Their special interest is prioritized over the interest of the collective, leading to a decrease of general welfare.

System capture

Example: in a movie club, 40% of people like comedy, 30% like drama, 30% like action.

Should they watch a comedy every time?

What if it was 60%, 20%, 20%?

System capture

A dictatorship system is captured by definition.
A majority vote can lead to capture
if the minority's opinion is consistently ignored.
Known as "tyranny of the majority".
It can affect legitimacy.

Random dictator

Whenever there is a decision to be made,
pick a person at random in the collective
and let them decide as a dictator.

Random dictator

Very efficient.
Very capture resistant (on average).
Terrible for stability.
Where is it used?

A random dictator system is captured in the short term, but it is highly resistant to capture in the long term. This is because every clique, even very small ones, will have their voice heard with a frequency proportional to the clique size.
In fact, a version of random dictator is used in most blockchain consensus protocol, both based in proof-of-work and proof-of-stake. We do this for efficiency, and because stability of block production is not a priority, while the highest priority is to resist capture by an adversarial minority.
This is because, if most block producers act honestly, then it is a Nash equilibrium to also act honestly when it is your turn to produce a block. But if a minority manages to capture the system for some amount of time, and arbitrarily decide on the content of a majority of blocks produced during this time, then the minority has an incentive to attack the network for personal gain.

Capture resistance vs. stability

A dictatorship is fully captured but also stable.
Direct democracy is at risk of capture, and still stable.
A random dictatorship is most resistant to capture, but unstable.

In this chart we consider the size of a clique or constituent, and plot it against the influence it will have over the collective decision in expectation.
For instance, if there is an unelected dictator then no clique, big or small, has any influence on decisions.
In a two-party system, only fairly large constituents will have a voice, while small constituents will have no voice.
If we elect a larger committee then smaller constituents are more likely to be represented and hence have an influence on the final decision.
Finally, in a random dictator system we have that every constituent, no matter how small, has a chance of influencing the final decision in proportion to the constituent size.
In general, we see that there is a trade-off between being resistant to capture and being stable.

Recap

Goals: utility, legitimacy and practicality.
In emergencies, practicality may be more relevant.
Simple direct democracy is legitimate, not so practical.
Dictatorship is practical, not legitimate.
Probably neither extreme maximizes utility.
With new technology, we have better tools & mechanisms to make direct democracy effective

Voting mechanisms

Widely used within decision-making systems.
Candidates to choose from: people, policies.
Voters who declare preferences through ballots.
A mechanism takes these ballots as input, and outputs a single candidate as the winner.
Many criteria to judge the mechanism.

New topic, wake up!
Voting mechanisms are some of the most popular ways to make collective decisions, and have been for centuries.
Why do you think that is? They are used for the election of leaders, for decision making within a governance body, choosing the winners in contests, among friends to decide on a restaurant, or in a family to name a dog.
Without a doubt, one of the most desirable criteria for a collective decision making mechanism is simplicity, meaning that it should be easy to understand and participate for the population. This is probably a big pro for voting mechanisms.
In the next slides we will explore some of the most popular voting mechanisms, along with some of the most popular criteria used to compare them.
What criteria do you think are most intuitive and desirable for a mechanism? Fairness? Proportionality? Utility? How would you define these terms precisely?

Voting mechanisms

We will see the following notions:

Single-vote mechanisms: plurality, two-round.
Ranked-vote mechanisms: Borda count, ranked-pairs.
Vote splitting, strategic voting.
Monotonicity criterion.

Single-vote mechanisms

Mechanisms where each voter picks one candidate.

Plurality voting: Candidate with most votes wins, even if they do not receive an absolute majority of votes.
Two-round voting: Top two candidates are voted on again. The candidate with most votes in second round wins.

Single-vote mechanisms

Plurality: 8 votes for A, 5 votes for B, 7 votes for C.

Two-round:

1st: 8 votes for A, 5 votes for B, 7 votes for C.
2nd: 8 votes for A, 12 votes for C.

	1st	2nd	3rd
8 voters	A	B	C
7 voters	C	B	A
5 voters	B	C	A

Recall that voters only vote for a single voter per round. But for convenience in what follows we assume we know the full candidate ranking of each voter, so we can analyze what would happen if any two out of the three candidates go head to head in the second round.
Are they equivalent? No. Look at the example above where there are three candidates A, B and C, and 20 voters with three types of preferences.
In plurality voting, we would only get to see the first column, and elect A with 8 votes.
In two-round, candidates A and C would go to second round, where the 5 voters in the last row would change their vote from B to C, and candidate C would win with 12 votes.
In general, several seemingly reasonable mechanisms result in different winners for the same collection of voters' preferences. This is why we need to look more closely into what properties we want out of a mechanism.

Vote splitting

Which of these mechanisms is better? Here is an argument against plurality voting.
In 2014, Candidate Chandu Sahu, from a political party called BJP in India, was a favorite to win in an election against opponent Ajit Jogi. To his surprise, on the day of the elections there were 10 other independent candidates registered with the same exact name. Apparently most of these candidates had no history in politics, but someone found them and offered them money to run on the elections. Of course, the obvious suspect is the opponent, but it was never proven. Luckily, the original Chandu Sahu still managed to win, but by only a razor-thin margin of 1200 votes, as the other 10 fake candidates accumulated around 70 thousand votes.
This technique is known as vote splitting, and plurality voting is well known to be susceptible to it.

Image source: https://indianexpress.com/article/political-pulse/the-10-other-sahus-how-namesakes-almost-cost-bjps-chandu-lal-sahu-a-win/

Vote splitting

Imagine B and C are similar candidates, and most people prefer either over A.
Known issue in plurality. Two-round helps alleviate it.

	1st	2nd	3rd
8 voters	A	B	C
7 voters	C	B	A
5 voters	B	C	A

Monotonicity criterion

A voter raising their rank for the winning candidate, or lowering their rank for a losing candidate, should not change the winner.
Plurality is monotonic, two-round voting is not.

Monotonicity Criterion

Two-round:

1st: 8 votes for A, 6 votes for B, 7 votes for C.
2nd: 11 votes for A, 10 votes for C.

	1st	2nd	3rd
6 voters	A	B	C
2 voters	A	C	B
3 voters	B	A	C
3 voters	B	C	A
5 voters	C	B	A
2 voters	C	A	B

Monotonicity Criterion

Bottom-row voters raise their preference for A.

Two-round:

1st: 10 votes for A, 6 votes for B, 5 votes for C.
2nd: 10 votes for A, 11 votes for B.

	1st	2nd	3rd
6 voters	A	B	C
2 voters	A	C	B
3 voters	B	A	C
3 voters	B	C	A
5 voters	C	B	A
2 voters	A	C	B

Strategic voting

A mechanism in which a voter increases the chances of a candidate by not voting for them.

Ranked-vote mechanisms

Mechanisms where each voter ranks all candidates.

In 1770, Jean-Charles de Borda showed 2-round may elect a candidate that would lose out head-to-head to every other candidate.

	1st	2nd	3rd
8 voters	A	B	C
7 voters	C	B	A
5 voters	B	C	A

Borda count

Each voter gives a rank of all $k$ candidates
Interpreted as if giving $k-1, k-2, \cdots, 1, 0$ points
Add up all points, select candidate with most points.
Borda count is monotone.

Borda Count

	2 points	1 point	0 points
8 voters	A	B	C
7 voters	C	B	A
5 voters	B	C	A

16 points for A, 25 points for B, 19 points for C.

Recap

Borda count is arguably more fair.
But plurality and two-round voting are simpler.
Simplicity seems to be important in practice.
No voting mechanism is perfect.

Goals clash

We mentioned that the main goals of a decision-making system are utility, legitimacy and practicality.

Can you think of real-life scenarios where these goals clash?

Sampling voters

In a country that runs referendums periodically, the turnout is only 2%, and older people tend to vote much more often than younger people.

The president changes the voting mechanism so that in each referendum, only 5% of the population elected uniformly at random is allowed to vote. As a result, every person is allowed to participate in one out of 20 referendums on average.

It is now observed that 80% of the people allowed to vote actually vote, so the global turnout grows from 2% to 4%. Moreover, the previously correlation between age and willingness to vote decreases considerably.

Would you support this new mechanism?

A holy grail

A "holy grails" of voting theory is finding a voting mechanism that simultaneously offers local privacy and global transparency: no one should be able to see another person's ballot, but enough aggregate information about the ballots should be public so that everyone can verify the correctness of the result.

Suppose such a mechanism is created using cryptography; however, it requires every voter to use a private key and be trained in the basics of cryptography. A nation's president proposes to use such a mechanism, but the feedback from the population is negative, because people don't trust digital voting or cryptography.

What goals are at odds here? What would you do as president?

Proof of Stake

In a Proof-of-stake (PoS) based blockchain network, validators are the nodes that participate in the consensus protocol and produce blocks. While it is possible to have a "pure" PoS mechanism where every token holder can participate in consensus directly (imitating PoW), most high-profile projects bound the number of validators that get to be active at any given moment.

Instead, these project opt for "representative democracy" and let token holders express their preferences for the set of active validators. Examples of blockchain projects that do this are: Polkadot, Cardano, Cosmos, EOS, Tezos and Tron.

What do you think are the main reasons behind this choice?

Secure Validators

We saw that it's critically important for security to ensure that the set of validators is not captured by an adversary. Suppose we succeed, so that a super majority of validators participate in consensus honestly.

A priori, the mechanism for electing validators can be completely independent of the mechanism for deciding on upgrades. However, some projects merge them together. In particular, consider a project that on any referendum, delegates the voting power of all the passive stakeholders to the set of validators.

Does this constitute capture of the governance body?

Can you think of examples where the interests of validators are markedly different from the interests of the collective?