# Exaggerated opinions

David Marsay djmarsay at dra.hmg.gb
Wed Apr 29 03:12:56 PDT 1998

```Dear Markus,

Thankyou for your response  (28 Apr 1998):

> The Dodgson method has two major problems:
> 1) It is NP-hard; i.e., the winner cannot be calculated in a
>    polynomial time.

It is true. However, if we can accept that Dodgson is otherwise good,
then maybe we can develop useful approximations.

> 2) It fails to meet clone criteria.
>
> Although -if the Dodgson method is used- it is difficult for the
> voters to vote tactically, it is very simple for the parties to
> manipulate the result of the elections by nominating clones.

Could you provide details?

One thing about Dodgson is that there are so many variants, some of
which use tie-breaks that are prone to clones. Personally, that
doesn't worry me to much. First-past-the-post is very much more
vulnerable.

I like what I call the 'maxpath' method for Dodgson. Create a
graph whose nodes are the options. Join pairs of nodes with directed
lines indicating the pair-wise majorities and their size. Now, a
directed sequence of directed lines starting at one node and ending
at another is a directed path. The 'force' of the path is the
smallest majority along the path. For each directed pair the
'path-majority' is the maximum force along any path from the start
to the end, less the maximum force in the opposite direction.

The maxpath winners (maybe 1) each have a path majority over
every non maxpath-winner, and are maxpath drawn/tied.

If we assume that ballots tie clones, then introducing clones simply
duplicates nodes and paths, with the cloned nodes being tied. Thus
Dodgson may clone winners, but does no harm.

Cheers.
--------------------------------------------------
Sorry folks, but apparently I have to do this. :-(
The views expressed above are entirely those of the writer
and do not represent the views, policy or understanding of
any other person or official body.

```