Disproportionality indexes and robustness of proportional allocation methods

Pennisi, Aline

doi:10.1016/s0261-3794(97)00052-8

Cited by 40 publications

(36 citation statements)

References 12 publications

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“…What have we added to Monroe's (1994) and Pennisi's (1998) earlier studies of disproportionality and malapportionment? First, we have updated and complemented the zoo of indices proposed and used by various researchers, pointing out parallel developments in measuring volatility and possible extension toward systematic measurement of vote splitting.…”

Section: Discussionmentioning

confidence: 99%

“…This approach is also discussed in Gallagher (1991). Pennisi (1998) uses the equivalent of 2 multiplied by S 2 /V, and also the same expression with the roles of seats and votes (x and y) reversed ('Equal Proportions'). The latter tends to infinity when a party with some votes obtains zero seats.…”

Section: Seven Pre-1990 Indices Of Deviation From Proportional Represmentioning

confidence: 99%

“…This is, in our notation, the 'L 1 -norm' used by Pennisi (1998). Where Li (1995) multiplies by x, Pennisi (1998) divides by x, thus enhancing the impact of small parties even more than is the case with D. 2 in terms of advantage ratios. This is, in our notation, the 'L 2 -norm' used by Pennisi (1998).…”

Section: Twelve Indices Proposed Since 1990mentioning

confidence: 99%

“…Where Li (1995) multiplies by x, Pennisi (1998) divides by x, thus enhancing the impact of small parties even more than is the case with D. 2 in terms of advantage ratios. This is, in our notation, the 'L 2 -norm' used by Pennisi (1998). Where 2 divides by x, this form divides by x 2 , thus enhancing the impact of small parties.…”

Section: Twelve Indices Proposed Since 1990mentioning

confidence: 99%

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Mapping the Indices of Seats–Votes Disproportionality and Inter-Election Volatility

2003

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A B S T R A C TMeasures of electoral system disproportionality and of party system volatility (as well as malapportionment and vote splitting) present similar statistical issues in terms of deciding what index is most appropriate, but it is not common to view indices of disproportionality and volatility as serving similar ends. Making use of 12 different criteria, we evaluate 19 indices that have been previously proposed as measures of either disproportionality of electoral seats-votes results or over-time volatility of party vote (or seat) shares. We suggest that, on balance, Gallagher's (1991) index, which has achieved increasing acceptance in the seats-votes literature on disproportionality (see esp. Lijphart, 1994) offers the most desirable combination of features, although the advantages it offers over the Loosemore-Hanby index are not large and are debatable. We also find that Dalton's principle of transfers presents an ambiguity when one party has a larger number of excess seats, while another has a larger proportion of them.KEY WORDS Ⅲ Dalton's principle of transfers Ⅲ malapportionment Ⅲ proportionality Ⅲ volatility of party shares Ⅲ vote splitting The Objective: Mapping the Measures of DiscordanceDeviation from proportional representation (PR) means the difference in party vote shares and party seat shares in some given election (v i versus s i ). Volatility of votes means the difference in party vote shares (v i ) from one election to another (v it versus v it' ); similarly, volatility of seats means the difference in party seat shares (s i ) from one election to another (s it versus s it' ). How do we best measure the proportionality/disproportionality of the translation of party vote shares into party seat shares in a given election?

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Section: Discussionmentioning

confidence: 99%

Section: Seven Pre-1990 Indices Of Deviation From Proportional Represmentioning

confidence: 99%

Section: Twelve Indices Proposed Since 1990mentioning

confidence: 99%

Section: Twelve Indices Proposed Since 1990mentioning

confidence: 99%

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Mapping the Indices of Seats–Votes Disproportionality and Inter-Election Volatility

2003

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“…parties with approximately 20% of the votes. It is known from other experimental studies that most of the known allocation methods tend (in various degrees) to be unfair and usually favour the larger parties [13]. It remains a question whether this pattern of voting influences the fairness of seat allocation.…”

Section: Allocation Of Seats In South Africamentioning

confidence: 99%

Fairness of seat allocation methods in proportional representation

Eck

Visagie

Kock

2005

ORiON

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In this paper the fairness of some methods of allocating seats in a proportional representation (PR) voting system is investigated. Different PR systems are in use throughout the democratic world, but the primary focus here is the method used in South Africa, namely the largest remainder method with a Droop quota. It is shown that as the number of parties increases, the number of lost votes (votes not used to allocate seats) increases when using this method. Other existing allocation methods are discussed and compared with each other as well as with three optimisation methods (based on mathematical programming) introduced in this paper. Applying these mathematical programming methods results in allocations that are more fair than the existing methods of seat allocation, if South African voting data are used. These mathematical models attempt to minimise a number of different measures of the deviation between the actual percentage of votes received and the percentage of seats allocated to a certain party. Ideally this deviation should be zero, but due to the discrete nature of seats this is virtually impossible to achieve.

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The Italian Bug: A Flawed Procedure for Bi-Proportional Seat Allocation

Pennisi¹

2006

Studies in Choice and Welfare

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Disproportionality indexes and robustness of proportional allocation methods

Cited by 40 publications

References 12 publications

Mapping the Indices of Seats–Votes Disproportionality and Inter-Election Volatility

Mapping the Indices of Seats–Votes Disproportionality and Inter-Election Volatility

Fairness of seat allocation methods in proportional representation

The Italian Bug: A Flawed Procedure for Bi-Proportional Seat Allocation

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