Dear Craig,
you wrote (25 Dec 2003):
> This can be named the Alternative Vote Twin Towers example: a support
> rise that is nearly 50% in size and that is entirely FPTP papers, is
> occuring while the candidate ('A') being supported changes into a
> loser:
>
> http://groups.yahoo.com/group/single-transferable-vote/message/244
>
> +-----------------------------------+
> |Winner: � �A� � �|Winner: � �B� � �| Alternative Vote winners
> +-----------------------------------+
> | Tot: � 513000� �| Tot: �1024001� �|
> +-----------------------------------+
> |� �A� � � 1001� �|� �A� � 512000� �| Change = +510999
> | * BA � � �999� �|� �BA � � 1001� �| Change = +2
> |� �CBA� � 1000� �| * CBA� � 1000� �|
> |� �DBA� � 2000� �|� �DBA� � 2000� �|
> |� �EBA� � 4000� �|� �EBA� � 4000� �|
> |� �FBA� � 8000� �|� �FBA� � 8000� �|
> |� �GBA� �16000� �|� �GBA� �16000� �|
> |� �HBA� �32000� �|� �HBA� �32000� �|
> |� �IBA� �64000� �|� �IBA� �64000� �|
> |� �JBA� 128000� �|� �JBA� 128000� �|
> |� �KBA� 256000� �|� �KBA� 256000� �|
> +-----------------------------------+
This is neither an example showing Alternative Voting violates
monotonicity nor an example showing Alternative Voting violates
participation. This is an example showing Alternative Voting
violates consistency. However, it has been demonstrated by
HP Young that only positional methods (e.g. FPP, Borda,
Approval Voting) satisfy consistency.
Markus Schulze
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