Comparisons: Droop Quota ~ Party Cloning 1

Susceptibility of Droop Quota Party-List Elections to Party Cloning

Party cloning threshold figures are introduced in the earlier Evaluations: Party Cloning section where the figures for CHPV are evaluated against those for an optimally proportional voting (OPV) system. The relevant threshold figures for the Droop Quota are derived using the same methodology as explained in this earlier section. For up to six winners, the benchmark OPV figures are repeated below left and the corresponding figures for the Droop Quota are shown below right.

To recap, the green line is the two-party map for parties A and B. The red line is the 1:1 two-way tie line for parties B₁ and B₂ on the three-party map for A, B₁ and B₂. The ranges of the tally shares for party B (t_B) that produce a different seat share for A:B (as stated in each domain) after party B clones itself into parties B₁ and B₂ are highlighted in white.

Any particular tally share threshold for party B may rise, fall or remain unchanged following its cloning attempt. Where it is a rise, party B succeeds only in harming its own chances. The black line within any white area indicates the change in the tally share threshold needed to maintain the (critical-tie) boundary between the two relevant seat share domains. It has a positive gradient for a rise in this threshold. Where it is a falling threshold, party B gains an unfair advantage over A. The black line now has a negative slope.

Regardless of the number of winners (W) in the Droop Quota Party-List election, it is immediately obvious that cloning by party B has no detrimental effect on party A. Each seat share domain boundary is either unchanged by the cloning or it moves such that B inflicts harm on itself. In this election scenario, the Droop Quota is hence not vulnerable to party-cloning strategic nominations.

In the previous Party-List Hare Quota section of this chapter, it is demonstrated that the Hare Quota is an optimally proportional voting (OPV) system. Therefore, the OPV threshold figures above left are also those for the Hare Quota. Further, the Hare and Droop Quota approaches are the two most common largest remainder party-list methods.

The Hare Quota has an optimality of 100% but it is readily susceptible to party cloning. In comparison, the Droop Quota is not as vulnerable to party cloning but it falls short of 100% optimality. There is clearly a trade-off between these two conflicting aspects. It depends on which feature is the more important for an election as to whether the Hare or Droop Quota is the better largest remainder method. In practice, the historically newer Droop Quota is far more popular than the original Hare Quota. Minimal susceptibility to cloning is usually considered to be more important than a marginal improvement in proportionality.

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