Representative Democracy - The Downsian Model

Utility or rent

Probability of coming to power

- Two parties A and B, announce a policy platform simultaneously and commit to it
- Both compete for political office and would like to come to power
- Do not have any ideological bias
- Recieve rent or utility from being in power

Assumes Condorcet winner and Median Voter Theorem applies

Median voter's bliss point, selecting it as their policy platform

Representative Democracy

Under specific assumptions, a Condorcet winner exists and coincides with the median-ranked bliss point.

Strategic voting

A strategy that gives a weakly higher/the same payoff than any other strategy regardless of others' choices.

A model where two parties compete for political office with announced policy platforms.

Open agenda decision choice

Citizens elect politicians who offer policy alternatives and make the policy choice.

Via the Democratic Index.

- A = 1 B = 0
- A = 0 B = 1
- A = 0.5 B = 0.5 (assuming that voters vote for one of the two parties indifferently, randomising btwn two parties if they have the same policy, there is single-peaked policy preferences, median-rankd bliss point by $P_m$)

- Suppose A and B want to deviate from $p_m$
- Assume arbitrarily that $p_a > p_b > p_m$
- One party can announce $p_m$. If party A does that, then $\mathbb{P}(P_A, P_B) = 1$
- Party B cannot win $(1 - \mathbb{P}(P_A, P_B) = 0)$ as long as $\mathbf{p}_b \neq \mathbf{p}_m$

- Hence, both parties converge to the bliss point of the median voter
- Indifference and random voting means $\mathbb{P}(P_A, P_B)' = 1 - \mathbb{P}(P_A, P_B) = \frac{1}{2}$ using the law of large numbers as long as parties offer the same policy