[EM] Proportional means equal portions of the whole.

[Tom Round]

1. One point of order: I don't take well to unfounded adverse speculation
about my personal motives or my commitment to the cause of fair elections,
whether written in prose or in haiku.

2. Donald claims that "A Hare STV election can give us near 100%
proportionality. 
 The proportionality of a Droop STV election will depend
on the number of seats, the more seats, the higher the level of
proportionality. For example: a Three seat district Droop STV election can
give us a near 75% proportionality, better than Plurality-At-Large, but not
as good as Hare STV." 

This impliedly argues that a Hare PR election gives 100% proportionality in
_all_ elections, regardless of how many seats are vacant, simply because the
Hare quota makes no (explicit) allowance for a near-quota of wasted votes. A
moment's reflection will show that this cannot be true. Even with the Hare
quota, is a election for 20 seats really no more proportional than an
election for 10 seats or 5 seats? Does Hare PR really guarantee 0% wastage
of votes regardless of whether the count is for 2 seats or 200 seats? The
answer is plainly no. The proportionality of an election rises in roughly
linear proportion to the number of seats on offer - just as much under the
Hare as under the Droop quota.

3. By the same token, do we have 100% proportionality if we use STV rules to
fill one seat? (In this case Hare and Droop operate the same as there is no
distribution of surplus votes.) Donald says that "A Plurality-At-Large
election can give us near 50% proportionality." But why not 100%? Why not
simply shift the goalposts so the quota is no longer 50.01% (that's the
dreaded and corruptly-devised Droop quota, remember), and continue
"low-man-out" transfers until the last candidate remaining has 100% of the
total votes? Then we could claim - according to Donald's logic - that
single-seat electoral districts (or three-seaters with Hare STV) give "more
exact proportionality" than, say, election results for the New South Wales
Legislative Council, where 21 seats are filled at each election by
Droop-quota STV. Does that seem correct?

4. Donald states that "One truism of Proportional Representation is that
members are to be elected by equal portions of total votes." I don't dispute
that. But Droop-quota STV doesn't violate this principle. In my 5-seat
example, 5 candidates are elected with an equal proportion of the total
votes (16.67% each) -- unlike, eg, Japanese-style Limited Vote. Under the
Hare quota, either we eliminate the last runner-up and transfer her votes
(even if they have a "choice" of ony one candidate to go to), so that each
elected candidate has exactly 20% (except Donald condemns this procedure
when used with Droop STV so we must conclude it is equally wrong if used
under Hare STV) -- or else we stop the count once no further eliminations
can affect the result, which will occur once the 5th candidate has as little
as 10.01% (which does NOT ensure that "members are elected by equal portions
of the total votes"). Either method is a violation of principles Donald has
advocated.

Oh, we can SAY "wait a moment, the 5th candidate hasn't reached quota yet,
she's not yet officially elected" but once she has more than half of the
votes remaining in the count (ie, not set aside as quotas for elected
candidates), it's all over bar the shouting. (Unless we allow seats to be
left vacant if so many votes exhaust that there are fewer than five full
quotas left at the end. What that would mean is that a nominally 5-seat
election using Hare STV would operate in practice effectively like a 4-seat
election using Droop STV.)

5. I really shouldn't need to repeat this point a third time, but it seems
necessary. Donald argues: "Transferring exhausted ballots to the remaining
candidates is a corrupt way of trying to fill up the quotas, it should not
be done." (I assume Donald is talking about "exhausted ballots" that still
have a preference for one or more elected candidates, and that he's not
mixing this up with the STV variant where completely exhausted ballots -
those with preferences only for defeated candidates - are deemed divided
equally among the remaining candidates in order to avoid having to
re-calculate the quota at each stage of the count.) Read my lips: 

*** But if we _don't_ keep eliminating _all_ the lowest candidates and
transferring their preferences (if any), until only the five (or whatever
number) elected candidates remain and every ballot has been allocated to its
highest preference (if any) among those five, then we _cannot_ make sure
that every elected candidate will have a full Hare quota. ***

Ie, if we _don't _ do what Donald has just condemned, we can end up with
this kind of result under the Hare quota: first four elected candidates, 20%
each; 5th elected candidate, 10.01%; exhausted votes (ie, those which refuse
to give any of the winning five candidates a preference), 9.99%. So much for
"equal portions of the total votes".

Even if those other 9.99% do give a preference for every candidate (as is
required by law in most Australian STV systems), so that their votes end up
raising the fifth candidate from 10.01% to 20.00%, this is symbolic only.
She was certain to be elected as soon as she passed 10.01% - only half a
quota, under Hare. Under Droop, the last candidate "past the post" is not
certain of election until he/she has won a full 16.67% quota.

6. Donald is correct on one point: it is a question of mathematics. However,
it is also a question where mathematical analysis and reflection correct,
rather than confirm, our initial intuitions (as Thomas Hare himself realised
when he abandoned the Hare quota and advocated the Droop quota). Likewise,
it would be much simpler and more intuitively correct if pi did equal
3.0000. Unfortunately, if we did construct our institutions based the
simpler assumptions like this, we would find there are certain real-world
consequences that may not be to our liking.

PS: Could I please have some feedback from others on the list as to whether
people are finding the arguments for the Droop of the Hare quota more
convincing.

At 04:48 22-10-99 -0400, you wrote:
>Greetings,
>
>     Proportional means equal portions of the whole.
>     One truism of Proportional Representation is that members are to be
>elected by equal portions of total votes.
>     Which means that when we reduce the candidates down to the elected
>members, their vote sums are to be near equal portions of the total votes,
>and the number of portions are to be equal to the number of seats.
>     No one has the right to suggest that members be elected by a number of
>votes less than an equal portion of total votes.
>     Part, share, and quota are other words that may be used in place of
>portion. Quota is the word we use when we are discussing proportional
>election methods. The word `quota' implies `No less than this amount'.
>(Quota: the share or proportion assigned to each in a division or to each
>member of a body) The word `assigned' implies: no less - no more. This is
>the intent of the Hare method, that members would be elected by the full
>Hare quota, or at least a near quota.
>     Quota is the proper word to use in regard to a proportional election
>method. In order for the method to be proportional it needs the quota to be
>filled. Anything that would cause the quotas to be less filled is something
>that is making the method less proportional. Exhausted votes and/or Droop
>quota and/or groups acting to lower the votes on their candidates, are all
>things that make the method less proportional.
>     Transferring exhausted ballots to the remaining candidates is a
>corrupt way of trying to fill up the quotas, it should not be done.
>
>     The vote sums of the elected members in a Hare STV election will be
>`equal parts of the whole' or at least near equal parts, provide we do not
>have too many exhausted ballots and/or groups do not lower the number of
>votes.
>     The vote sums of the elected members in a Droop STV election cannot be
>equal parts of the whole. Droop has this residue of an extra quota of votes
>- an extra part. There can be no equal parts of the whole if the whole is
>divided by a number that contains an extra part.
>   The reason is math.
>   Mathematically, the addition of the extra part is not proportional.
>   The addition of the extra part is political.
>   Droop supporters are mixing math and politics.
>   Math is math and the residue of an extra quota is an embarrassment.
>
>     In order to give you some comparison of proportionality, consider
>three election methods.
>     A Hare STV election can give us near 100 % proportionality.
>     A Plurality-At-Large election can give us near 50 % proportionality.
>     The proportionality of a Droop STV election will depend on the number
>of seats, the more seats, the higher the level of proportionality. For
>example: a Three seat district Droop STV election can give us a near 75 %
>proportionality, better than Plurality-At-Large, but not as good as Hare
>STV.
>     A nine seat Droop STV election can give us near 90 % proportionality,
>so if you must have the Droop quota, then use it with a high number of
>seats per district.
>     Meek STV using hare Quota at the start of the count is the best STV.
>It will give us 100 % proportionality, but it needs computers. Now, it is
>true that goroups may still attempt to lower the number of votes they place
>on their candidates, but they cannot stop the addition of transfer votes
>from increasing the numbers towards the Hare Quota.
>     This is the best that can be done with STV. To get something better we
>need to go to some type of Method that will balance up the proportionality.
>The flaw of MMP can be solved by using only one vote per person instead of
>two, but that is another discussion.
>
>     The last word on the proportionality of STV: Anyone who supports
>actions to lower the proportionality of STV cannot honestly claim to
>support proportional representation.
>
>Regards,
>Donald
>
>
>   +=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+
>   |                         Q U O T A T I O N                         |
>   |  "Democracy is a beautiful thing,                                 |
>   |       except that part about letting just any old yokel vote."    |
>   |                            - Age 10                               |
>   +=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+
>
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Tom Round, BA (Hons), LL.B,
Research Officer, Key Centre for Ethics, Law, Justice & 
Governance (KCELJAG), Griffith University,
Queensland 4111, Australia
ph (07) 3875 3817, fax 3875 6634