Electoral Systems: Proportional Systems

Additional Member System (AMS)

• Hybrid Nature: AMS is a 'mixed' system that combines a majoritarian element (First-Past-The-Post) with a proportional 'top-up' list to correct imbalances.
• Two-Vote Mechanism: Voters cast two separate ballots: one for a local constituency representative and one for a regional party list.
• D'Hondt Formula: This mathematical divisor method is often used to allocate regional seats by dividing a party's list votes by the number of seats they have already won plus one ($V / (s+1)$).

Single Transferable Vote (STV)

• Ordinal Voting: Voters rank candidates in order of preference (1, 2, 3...) rather than choosing just one, providing high levels of voter choice.
• The Droop Quota: To be elected, a candidate must reach a specific threshold of votes calculated by the formula:

$Quota = \left( \frac{\text{Total Valid Votes}}{\text{Seats} + 1} \right) + 1$

• Transfer Mechanism: If a candidate exceeds the quota, their surplus votes are transferred to the voters' next preferences; if no one meets the quota, the lowest-ranked candidate is eliminated and their votes are redistributed.

• AMS vs. STV: AMS maintains a direct link between a single representative and a local area, whereas STV prioritizes overall proportionality and voter choice between candidates of the same party.

• Closed vs. Open Lists: In AMS, the party usually determines the order of candidates on the list (Closed), while STV effectively functions as an open system where voters decide which specific individuals are elected.

• Master the Droop Quota: Always remember the '+1' in both the denominator and the final result of the Droop formula; forgetting these is a common source of calculation errors.

• Analyze the 'Top-Up': When discussing AMS, focus on how the regional seats act as a corrective mechanism for the 'winner-takes-all' distortions of the constituency seats.

• Evaluate Government Stability: Be prepared to argue both sides of the coalition debate; while coalitions are more representative, they can lead to slower decision-making or 'deadlock'.

• Check District Magnitude: If an exam question asks why a system isn't perfectly proportional, look at the number of seats per district; fewer seats per district usually favor larger parties.

• The 'Complexity' Myth: While the mathematical allocation (like D'Hondt or Droop) is complex for officials, the act of voting (ranking or two votes) is relatively straightforward for the citizen.

• Assuming Weak Government: A common misconception is that PR always leads to weak government; however, many stable democracies use PR to foster long-term policy consistency through consensus.

• Wasted Votes in PR: Students often think PR eliminates wasted votes entirely; in reality, votes for parties that fail to meet a threshold or 'surplus' votes in poorly designed systems can still be 'wasted'.