Seminar 5 – Spatial Theory
It is important to be familiar with the spatial model because:
It is important to know which institution is most important to lobby.
Analyse the actors who have power and who we need to target our nonmarket strategy.
Predict the outcome of the policymaking process.
Part I – Spatial Theory of Voting: One Dimension
- Utility functions and sets in one dimension
- Condorcet winner and Black’s MVT
Policies as points in space
We first need to see policy alternatives as points in space, but this is something we do every
day because conventional politics are one dimensionally organised from left to right.
But policy positions can also be placed in a two-dimensional space, e.g., stances of MEPs on
European integration and climate action.
The issue doesn’t need to be about politics. It can be about buying a car among a group of
friends and choosing whether we want a less quality or higher quality car.
Main take away: policy preferences, about any issue can be placed in a one-dimensional or
two-dimensional line.
,Preliminaries: Utility
Utility function: we show the preference of a specific policymaker through the utility
that they receive from this preference.
o We define a utility function U as follows the utility of proposal y = U(y) =
(level of satisfaction).
Preference: if a person likes one alternative more than the other, then both of the
following must be true:
o If the person (strictly) prefers y to z, then U(y) > U(z).
o If U(y) > U(z), then the person prefers y to z.
Indifference: if a person likes two alternatives equally well, then both of the following
must be true:
o If U(y) = U(z), then the person is indifferent between z and y.
o If the person is indifferent between z and y, then U(z) = U(y).
Representing utility functions:
How does the utility function slope? Non-satiable utility function (often used for
consumer behaviour in economics).
o For every product (X) that you consume, your utility increases The
assumption behind this utility function is that the more I consume, the higher
my utility will be. It doesn’t increase.
o The more you consume, utility keeps increasing but at a slower rate until it
becomes flat.
o If we have such a utility function, the indifference curve of the function will
slope like in the non-satiable utility function graph.
Satiable utility function used for legislator behaviour in political economy.
o If we assume that politicians do not care about the number of votes they get and
will care about the policy outcome, politicians have in mind an ideal policy.
o E.g. politician A prefers a budget of 50. If they get their ideal policy, their utility
function is high but afterwards it goes down.
o The closer the policy outcome is to the ideal policy of the politician, the closer
it is to utility. The further away the outcome, the lower the utility.
, Key elements of a spatial analysis of politics
1. Preferences: ideal point and utility function.
2. Represent issue alternatives on the line.
3. Rules by which alternatives are voted on voting rule (e.g., majority voting, QMV,
agenda-setter, etc.).
1. Preferences
Preferences are spatial and all alternatives can be described spatially.
Two components of voters need to be specified: the ideal point and the utility function.
The ideal point is simply the policy that the voter would most want enacted:
o It may be an actual number, such as the size of the budget, but it can also be
more abstract such as a location on the liberal-conservative ideological scale.
The utility function describes how much pleasure the voter receives from policies, as
a function of how far the policy is located from the voter’s ideal point.
The assumption is that preferences are single-peaked and symmetric:
o The policymaker has an ideal point and its utility declines at the same rate,
regardless of direction = preferences are said to be Euclidean
o This implies that preferences are a decreasing function of the distance between
the policy outcome and the policymaker’s ideal point. Utility depends on the
distance between the outcome and your ideal point as a legislator.
These are two different functional forms:
Both describe single-peakedness: there is one high levelness of utility.
Both describe symmetry this means that if you go away from your ideal point, your
utility declines at the same rate, regardless of whether you go more to the right or to the
left.
It is important to be familiar with the spatial model because:
It is important to know which institution is most important to lobby.
Analyse the actors who have power and who we need to target our nonmarket strategy.
Predict the outcome of the policymaking process.
Part I – Spatial Theory of Voting: One Dimension
- Utility functions and sets in one dimension
- Condorcet winner and Black’s MVT
Policies as points in space
We first need to see policy alternatives as points in space, but this is something we do every
day because conventional politics are one dimensionally organised from left to right.
But policy positions can also be placed in a two-dimensional space, e.g., stances of MEPs on
European integration and climate action.
The issue doesn’t need to be about politics. It can be about buying a car among a group of
friends and choosing whether we want a less quality or higher quality car.
Main take away: policy preferences, about any issue can be placed in a one-dimensional or
two-dimensional line.
,Preliminaries: Utility
Utility function: we show the preference of a specific policymaker through the utility
that they receive from this preference.
o We define a utility function U as follows the utility of proposal y = U(y) =
(level of satisfaction).
Preference: if a person likes one alternative more than the other, then both of the
following must be true:
o If the person (strictly) prefers y to z, then U(y) > U(z).
o If U(y) > U(z), then the person prefers y to z.
Indifference: if a person likes two alternatives equally well, then both of the following
must be true:
o If U(y) = U(z), then the person is indifferent between z and y.
o If the person is indifferent between z and y, then U(z) = U(y).
Representing utility functions:
How does the utility function slope? Non-satiable utility function (often used for
consumer behaviour in economics).
o For every product (X) that you consume, your utility increases The
assumption behind this utility function is that the more I consume, the higher
my utility will be. It doesn’t increase.
o The more you consume, utility keeps increasing but at a slower rate until it
becomes flat.
o If we have such a utility function, the indifference curve of the function will
slope like in the non-satiable utility function graph.
Satiable utility function used for legislator behaviour in political economy.
o If we assume that politicians do not care about the number of votes they get and
will care about the policy outcome, politicians have in mind an ideal policy.
o E.g. politician A prefers a budget of 50. If they get their ideal policy, their utility
function is high but afterwards it goes down.
o The closer the policy outcome is to the ideal policy of the politician, the closer
it is to utility. The further away the outcome, the lower the utility.
, Key elements of a spatial analysis of politics
1. Preferences: ideal point and utility function.
2. Represent issue alternatives on the line.
3. Rules by which alternatives are voted on voting rule (e.g., majority voting, QMV,
agenda-setter, etc.).
1. Preferences
Preferences are spatial and all alternatives can be described spatially.
Two components of voters need to be specified: the ideal point and the utility function.
The ideal point is simply the policy that the voter would most want enacted:
o It may be an actual number, such as the size of the budget, but it can also be
more abstract such as a location on the liberal-conservative ideological scale.
The utility function describes how much pleasure the voter receives from policies, as
a function of how far the policy is located from the voter’s ideal point.
The assumption is that preferences are single-peaked and symmetric:
o The policymaker has an ideal point and its utility declines at the same rate,
regardless of direction = preferences are said to be Euclidean
o This implies that preferences are a decreasing function of the distance between
the policy outcome and the policymaker’s ideal point. Utility depends on the
distance between the outcome and your ideal point as a legislator.
These are two different functional forms:
Both describe single-peakedness: there is one high levelness of utility.
Both describe symmetry this means that if you go away from your ideal point, your
utility declines at the same rate, regardless of whether you go more to the right or to the
left.
