Rational Choice
Theory
In this part of the course we will discuss two areas of rational choice theory, which is the study of
rational decision making. We will introduce:
1. Social choice theory, the study of collective decision making based on individual preferences
2. Decision theory, the study of individual decision making given various possible actions and
outcomes
We will consider some:
basic tools and concepts of these fields
everyday applications of the tools
attempts to use the tools to solve deep problems
critical reflections on these tools
1: Social Choice Theory
Why study social choice theory? To understand how voting works and how it can truly reflect the
“will of the people”.
Voting is a key component of the political system of democracy (“demo” is the ancient Greek word
for “the people”, and “kratos” means “power”)
A political system in which the authority of the government comes from the people as a
whole
The two main justifications given for the strategy of voting are that:
1. It reveals the “will of the people”, what the people as a whole want
2. It tends to produce good results
Some thinkers say that the combination of many perspectives from people with diverse
experiences, beliefs, desires and temperaments yields an all-encompassing view which
includes all perspectives, and which a smaller group would not have.
Social choice theory (SCT) studies how information should be collected from individual voters, and
how it should be best aggregated (i.e. put together) in order to truly represent the population’s
“will”.
In order words, SCT studies methods of collective decision-making based on individual
preferences
It is unclear whether there can be one correct method for determining the true will of the people, or
whether each simply has features that make it more, or less, suited to particular contexts and
situations.
In SCT, “voting” refers to the act of an individual expressing their preferences, rather than simply the
physical act of casting a ballot.
,SCT studies the features of a voting system at a general level – voting in any context.
Framework for studying SCT
Each individual gets their own column, under which their preferences are
listed. The first on the list is their first choice, the second their second,
etc.
In this example, each individual has voted for their favourite fruit.
Each option (a, b, or c) is an abbreviation of a type of fruit. For example, “a” stands for “apple”.
Using a social choice rule, these individual preferences will be aggregated into one “social
ordering” – a representation of the group’s preferences:
SCT terminology
Individuals choose from options. For example, a particular political candidate would be considered
an option
Each individual’s choices are summarised as an individual ordering (a list of their preferences)
All the individual orderings are put side by side as a profile. A profile is, in other words, a set of all
the individual orderings from the group
The profile is converted into a social ordering (list of the group’s aggregated preferences) using a
specific social choice rule
In other words, we decide on the preferences for the group as a whole by considering the
preferences expressed by all the individuals, and then use a rule for generating a social ordering
from this information
Individual orderings x 3 = a profile + social choice rule = social ordering
Condorcet social choice rule
The options are put into pairs, and then the winner of that pair is put higher up in the social
ordering.
a VS b, b VS c, and a VS c. Every time, for example, a is preferred to b, it receives a “point”. The
points are then tallied and the option with the most points becomes the first choice in the social
ordering.
We must first take the options one pair at a time, and identify, for each pair, which option is
preferred more often.
, Ties
When one option is preferred equally to another. Indicated by having the options placed directly
next to each other within an individual ordering.
When an option is tied with another, neither receives a “point”.
There can also be ties within the social ordering.
Benefits of the Condorcet rule
1. Anonymity: each individual’s ordering is treated the same, no one person’s vote is
considered more or less important/influential than another’s.
2. Neutrality: each option is given equal weighting.
Both promote fairness and equality
Downsides of the Condorcet rule
1. Anonymity: equality of votes in some contexts is not appropriate. For example, specialists or
experts might deserve more power than others. Or people who are representatives of the
region which would be most affected by a vote. In cases like these, it is appropriate to give
certain voters special consideration by treating them differently to others.
2. Neutrality: there are also some contexts in which neutrality may not be fair. For example,
the votes needed to change something as important as the constitution should be greater
than the votes required for it to remain the same. In other words, it should be harder to
change the constitution than to not change it. This is because the constitution is:
Fundamental
Deeply-considered
Consequences are far-reaching
3. It can be difficult to apply the rule when the number of options is high: as the number of
options increases, the numbers of pairs rises rapidly. This isn’t much of a problem if you’re
able to automatically apply the Condorcet rule.
4. It sometimes generates cycles
Cycles
When there is no best option (no option at the top of the social ordering): for each option, there is
another than it is preferred to
There is no option which is preferred. This can be represented as a triangle, with
arrows pointing towards the option which is preferred over the option on the other
end. The position of each option in the triangle doesn’t matter, they could go
anywhere.
To many thinkers, a cycle is absurd, i.e. deeply irrational. The result is that it is
unclear which option to choose over another.
Theory
In this part of the course we will discuss two areas of rational choice theory, which is the study of
rational decision making. We will introduce:
1. Social choice theory, the study of collective decision making based on individual preferences
2. Decision theory, the study of individual decision making given various possible actions and
outcomes
We will consider some:
basic tools and concepts of these fields
everyday applications of the tools
attempts to use the tools to solve deep problems
critical reflections on these tools
1: Social Choice Theory
Why study social choice theory? To understand how voting works and how it can truly reflect the
“will of the people”.
Voting is a key component of the political system of democracy (“demo” is the ancient Greek word
for “the people”, and “kratos” means “power”)
A political system in which the authority of the government comes from the people as a
whole
The two main justifications given for the strategy of voting are that:
1. It reveals the “will of the people”, what the people as a whole want
2. It tends to produce good results
Some thinkers say that the combination of many perspectives from people with diverse
experiences, beliefs, desires and temperaments yields an all-encompassing view which
includes all perspectives, and which a smaller group would not have.
Social choice theory (SCT) studies how information should be collected from individual voters, and
how it should be best aggregated (i.e. put together) in order to truly represent the population’s
“will”.
In order words, SCT studies methods of collective decision-making based on individual
preferences
It is unclear whether there can be one correct method for determining the true will of the people, or
whether each simply has features that make it more, or less, suited to particular contexts and
situations.
In SCT, “voting” refers to the act of an individual expressing their preferences, rather than simply the
physical act of casting a ballot.
,SCT studies the features of a voting system at a general level – voting in any context.
Framework for studying SCT
Each individual gets their own column, under which their preferences are
listed. The first on the list is their first choice, the second their second,
etc.
In this example, each individual has voted for their favourite fruit.
Each option (a, b, or c) is an abbreviation of a type of fruit. For example, “a” stands for “apple”.
Using a social choice rule, these individual preferences will be aggregated into one “social
ordering” – a representation of the group’s preferences:
SCT terminology
Individuals choose from options. For example, a particular political candidate would be considered
an option
Each individual’s choices are summarised as an individual ordering (a list of their preferences)
All the individual orderings are put side by side as a profile. A profile is, in other words, a set of all
the individual orderings from the group
The profile is converted into a social ordering (list of the group’s aggregated preferences) using a
specific social choice rule
In other words, we decide on the preferences for the group as a whole by considering the
preferences expressed by all the individuals, and then use a rule for generating a social ordering
from this information
Individual orderings x 3 = a profile + social choice rule = social ordering
Condorcet social choice rule
The options are put into pairs, and then the winner of that pair is put higher up in the social
ordering.
a VS b, b VS c, and a VS c. Every time, for example, a is preferred to b, it receives a “point”. The
points are then tallied and the option with the most points becomes the first choice in the social
ordering.
We must first take the options one pair at a time, and identify, for each pair, which option is
preferred more often.
, Ties
When one option is preferred equally to another. Indicated by having the options placed directly
next to each other within an individual ordering.
When an option is tied with another, neither receives a “point”.
There can also be ties within the social ordering.
Benefits of the Condorcet rule
1. Anonymity: each individual’s ordering is treated the same, no one person’s vote is
considered more or less important/influential than another’s.
2. Neutrality: each option is given equal weighting.
Both promote fairness and equality
Downsides of the Condorcet rule
1. Anonymity: equality of votes in some contexts is not appropriate. For example, specialists or
experts might deserve more power than others. Or people who are representatives of the
region which would be most affected by a vote. In cases like these, it is appropriate to give
certain voters special consideration by treating them differently to others.
2. Neutrality: there are also some contexts in which neutrality may not be fair. For example,
the votes needed to change something as important as the constitution should be greater
than the votes required for it to remain the same. In other words, it should be harder to
change the constitution than to not change it. This is because the constitution is:
Fundamental
Deeply-considered
Consequences are far-reaching
3. It can be difficult to apply the rule when the number of options is high: as the number of
options increases, the numbers of pairs rises rapidly. This isn’t much of a problem if you’re
able to automatically apply the Condorcet rule.
4. It sometimes generates cycles
Cycles
When there is no best option (no option at the top of the social ordering): for each option, there is
another than it is preferred to
There is no option which is preferred. This can be represented as a triangle, with
arrows pointing towards the option which is preferred over the option on the other
end. The position of each option in the triangle doesn’t matter, they could go
anywhere.
To many thinkers, a cycle is absurd, i.e. deeply irrational. The result is that it is
unclear which option to choose over another.
