For a constitutional amendment or any analogous (yea or nay) procedure,
there is a compelling theoretical reason not to round at all.  This is just
that the rules require the number of votes to meet or exceed a threshold in
order for the amendment to pass, and rounding would change the threshold and
thus break the rule.

Suppose you have 200 eligible voters and the rules require a 2/3rds vote for
passage.  Suppose the proposed amendment gets 133 votes.  133/200 = 66.5%.
66.5% is less than two thirds, so the amendment fails.  Rounding the vote to
67% would effectively change the rule to require a 66.5% vote instead of
two-thirds.

Note that the rule for a yea or nay procedure has to be that you _do not_
round, not that you round down.  If a deliberative body has a rule requiring
a 1/3rd vote to open a new proposal for debate, then an unrounded 33.4% vote
is successful, but rounding the result down would break the rule.


--
Matthew DeBell, Ph.D.
Director of Stanford Operations for the American National Election Studies
Institute for Research in the Social Sciences
Stanford University

650-725-2239
[log in to unmask]


> -----Original Message-----
> From: Political Methodology Society [mailto:[log in to unmask]]On
> Behalf Of Paul Gronke
> Sent: Thursday, May 22, 2008 12:06 PM
> To: [log in to unmask]
> Subject: [POLMETH] Rounding Up or Down in Voting Systems
>
>
> Suppose you have a constitutional amendment under consideration in an
> organization.  Passage of the amendment requires an affirmative vote
> of 2/3 of the eligible voters.
>
> The question I have regards rounding: do you round up or down for
> either of the calculations?
>
> I would have thought the answer straightforward until I did a bit of
> research into the d'Hondt and Lague PR formulae.  In all cases that I
> have found, the formula round DOWN in order to calculate quotas.
>
> Is there a theoretical or practical reason for always rounding down in
> these formula?  Would there be a reason for doing so in passing a
> constitutional amendment?
>
> ---
> Paul Gronke                Ph:  503-517-7393
> Professor                     Fax: 734-661-0801
> Reed College
> 3203 SE Woodstock Blvd.
> Portland OR 97202
>
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