# Bottoms Up for Herman Beun

Norman Petry npetry at sk.sympatico.ca
Wed Jul 29 17:22:05 PDT 1998

```Herman,

So far, I've seen three proposals on this list that seem reasonable, and at
least partially satisfy your basic goal, which is to create a rank ordering
of candidates that will provide proportional representation of party members
within their caucus no matter how many candidates are elected by the public.
I'll label these, for the purposes of discussion:

1) Bottoms-Up [HB] - your proposal.  Thanks to Don Davison for finding the
2) Ranked STV [MO] - Mike Osipoff's refined form of Ranked STV (July 27:
"Refinement to Proposal", and July 27: "Building the Party List")
3) Ranked STV [NP] - my proposal from July 28th.

I just gave my method and Mike's the same name, as they're virtually
identical in their practical effects and basic workings.  As you correctly
pointed out, conventional STV only provides a set of winners, and it's
erroneous to infer from their order of election (or defeat) any sort of rank
ordering of candidates.  Therefore, the term "Ranked STV" would seem to
provide the necessary distinction.  BTW, I'd be amazed if my proposal
(probably not Mike's - his has too many interesting quirks!) hadn't been
suggested before.  References, anyone?

***

Analysis of Ranked STV [MO]:

I can understand the logic behind Mike Osipoff's proposal for a refined form
of Ranked STV in which the current set of candidates chosen by STV is given
priority: it is intended to produce the most proportional outcome possible
for likely cases.  My Ranked STV proposal will occasionally produce a result
which is less accurate than conventional STV would have been, had the number
of caucus seats been known in advance.  For example, although this may seem
odd, a group of STV voters who would elect candidates:

{A,B,C,D}

if four seats are available, could instead elect candidates:

{A,B,C,E,F}

if five seats are available.  Unfortunately (?), using my system of Ranked
STV, this becomes impossible.  The system ensures that candidate D, who was
elected in the fourth STV election round, is protected from defeat, so the
result must be:

A,B,C,D,?

where "?" is probably (but not necessarily) E or F.  Mike's system does not
necessarily do this.  In his stage 5, if the STV count indicates that a more
accurate result is:

{A,B,C,E,F}

and provided that E>F (by Condorcet's rule) and the party (D66) won 5 or
more seats in the last parliament, then his 5th stage ranking becomes:

A,B,C,E,F.

Now, if D66 actually _does_ win exactly 5 seats (hopefully they'll do better
than that!), then Ranked STV [MO] will produce a more accurate (or at least,
more STV-like) result than Ranked STV [NP].  This potential improvement
comes at a price, however.  Aside from the obvious increase in the
complexity of the voting rule used to produce this result, is the loss of
"house-monotonicity".  In the above example, candidate D _must_ still be
elected in stage 5 (for house-monotonicity), yet Mike's method is in fact
designed to (potentially) elect candidates other than D, if the result
provides more accurate representation.  It seems to me that Ranked STV [MO]
will only produce a result different from Ranked STV [NP] when more than one
new candidate appears in the latest STV count, and the only way to add them
all is by removing one or more candidates ranked previously.  Therefore,
Ranked STV [MO] necessarily violates house-monotonicity in cases where it
produces a result different from Ranked STV [NP].

Now maybe, house-monotonicity isn't that important.  I do think the
increased rule complexity of Ranked STV [MO] _is_ a drawback, though, and
should be justified by some significant advantages.  Also -- perhaps this is
only an aesthetic consideration, but I dislike the idea of a decision made
by one polity (the ranked list, made by members of D66) formally depending
on a historical decision made by a different polity (the number of seats
allocated to D66 by the Dutch public in the last national election).  To me,
it seems better if these two decisions remain independent (Ranked STV [MO]
changes its selection method once the previous number of caucus seats has
been reached).

***

Which method to choose?

As Mike has pointed out here before in discussion of single-winner methods,
choosing the "best" method is not just a question of picking the method
which is most technically perfect.  Instead, it involves balancing the need
to satisfy important criteria (so the method produces good results) with the
practical need for a method that will be understood and accepted as fair by
most voters, in order to have it actually adopted by them (this usually
requires clear, simple rules).  This is why the election-methods list
proposed both Condorcet[EM] and Smith//Condorcet[EM] (and should probably
also propose Tideman[a sensible variant not involving margins] and then
Schulze) as single-winner methods to electoral reformers.  Depending on how
sophisticated the electorate is, any of these methods could potentially be
the "best" choice.  Each of these methods improves in technical perfection
over that preceding it, at the cost of increased rule complexity.  A guiding
maxim in selecting a voting rule should therefore be: "As simple as
possible, but no simpler".

Bottoms-Up [HB] is in my view _too_ simple.  Although it is a definite
improvement over Borda (almost anything is!), and will usually provide rough
proportionality as long as voting is sincere, it is manipulable, as I
demonstrated in my previous post.  Factions can gain an unrepresentative
share of caucus seats by spreading their votes evenly among all the
candidates who are members of that faction.  This is an important thing to
avoid if possible, since a method which can give an unfair advantage to a
few insincere voters will eventually lead to strategic, insincere voting by
most voters, thereby making the final results questionable (differences
between candidates belonging to each faction will tend to be "hidden" by the
voters, with the result that although factions gain proportional
representation, the best individual candidates within each faction are not
necessarily elected).  Ranked STV (mine or Mike's) doesn't have this
problem, so it's more likely to elicit sincere voting even once your party's
voters become more sophisticated.  Like conventional STV, these methods are
highly resistant to manipulation.

Ranked STV [MO] is, I think, not simple enough.  Too high a price is paid in
rule complexity for the extremely small potential gain in accuracy over
Ranked STV [NP].  One would have to run computer simulations to determine
how frequently Ranked STV [MO] would produce a result different from Ranked
STV [NP], but my guess would be probably fewer than 1 in a 100 cases.  Even
among these, the chances are small that the ranking difference would
actually produce a different caucus (since unless the ranking variations
straddle the actual number of seats your party wins, the result is the
same).  If I'm correct, the increased rule complexity of Mike's refined
method seems unjustified.  Furthermore, Mike's method will only produce a
result different from mine when it violates house-monotonicity -- probably a
dubious achievement among those who judge voting methods based on technical
criteria.

Not surprisingly then, I think that Ranked STV [NP] would be the best choice
for preparing your party's list.  It provides intra-party proportionality
(your main requirement, and the reason you want to replace Borda) while
maintaining simple, consistent rules.  Also, if you or your party members
care about technical criteria, this method _is_ house-monotonic.
Unfortunately, although the rules are simple, the count itself using this
method (or Mike's) is long and tedious to carry out by hand (STV is bad
enough, but to do it, say 60 or 70 times among thousands of ballots would
be appalling...).  Therefore, if for some reason you absolutely _must_ do a
hand count, your original method is probably a better choice (unless the
Dutch are a lot more patient than we Canadians!).

***

One final clarification: although I did suggest earlier that a good
single-winner method could be used to pick the top-ranked candidate, I'm not
recommending it now for the same reason I don't recommend Ranked STV [MO] --
the increased rule complexity is not justified.  For a party which routinely
elects 10 or more candidates, the chance that the Condorcet winner would not
be among that selection anyway is infinitesimal.  Be optimistic, and hope
that the fortunes of D66 never fall to the point where it _would_ matter!
It's better to use a good single-winner method for situations where
single-winner outcomes are important, such as the selection of your party

I hope you find some of this analysis useful.

Norm Petry

-----Original Message-----
From: Herman Beun <chbeun at worldonline.nl>
To: election-methods-list at eskimo.com <election-methods-list at eskimo.com>
Date: July 28, 1998 8:00 AM
Subject: Re: Bottoms Up for Herman Beun

>Dear Donald,
>
>>      That system is known as Bottoms Up in Australia. I know
>> that it has been used there - it may still be in use there.
>
>This is great! If it has a name, it must be good ;-) Although, with
>_this_ name I might still have some difficulty convincing my fellow
>party members that it is a really serious thing. :-) (Too bad, on the
>other hand, that I was not the first to invent this system)
>
>Do you (or anyone else) have any more details of this system, where
>has it been used, when, is it still being used in Cambridge MA or
>other places, any literature references (preferably "web-ised")?
>
>>      Once you have you party list of candidataes, you can test
>> the system by picking any number of seats and then going back
>> and running the data of the 3000 ballots as a STV election -
>> this will tell you how close your list comes to STV.
>
>Indeed, this would be the ultimate and convincing test. I am trying
>to get hold of the raw results of the last internal candidate
>elections, since I'd like to compare STV (i.e. Bottom Up) to the
>current Borda results in internal publications.
>
>Regards,
>
>Herman
>
>---------------------------------------------------------------------
>Herman Beun                                                    Arnhem
>http://home.worldonline.nl/~chbeun/                        Gelderland
>CHBeun at worldonline.nl                                       Nederland
>                                                                   EU
>**** Representative democracy is a contradiction in 4 year terms ****
>---------------------------------------------------------------------
>

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