Re: approximate solutions

From: laird popkin <lairdp_at_gmail_dot_com>
Date: Sat Jul 22 2006 - 00:26:05 CDT

While a chart is great to _illustrate_ the relationships between the
variables, as a math major, I'd agree with Ed that they're just an
illustration, and say that it would be much better to present the required
sample size given the various inputs as a formula (if possible, and it seems
to me that it ought to be) because it's much easier to analyze, and thus
trust, a formula than a computer program. Computer programs typically are
great for validating models (e.g. monte carlo simulations) but aren't a
great way to prove things in an absolute sense. And while graphs are great
for showing relationships, if people actually use graphs to look up values
it's slow and error prone. Imagine if people had to look up their tax rates
on a chart to fill out their income taxes. :-) A formula, and perhaps
pre-calculated reference tables, would be ideal.

To illustrate the relationships between the variables, you don't need to
graph all of the combinations. You could do a reasonable job of a basic
sensitivity analysis with only four graphs (e.g. "typical values for three
inputs, then chart the fourth input against the confidence level", for each
of the four inputs). Most business sensitivity analysis are worked out to
this level, as it's enough to answer questions like "how do my assumptions
of the maximum rate of margin-shifting per machine affect the required vote
count audit sample size?"

To be more thorough, such as for a deeper academic analysis, you might want
to show all combinations of three values per input (min, mean and max, for
example). That would be 108 charts (3*3*3*4), which nobody would ever read.
But you could put three lines on each chart (i.e. the lines for the
min/mean/max of one of the inputs, or "family of curves" you mentioned) and
that would get you down to 36 charts, which is (IMO) manageable for a
detailed, academic analysis.

Hmm. I don't know whether than explanation of how the charting could be done
is sufficiently clear. If you can send me the confidence formula, I can
quickly generate a set of the charts as I've described, so that you can see
what I'm talking about. If the "formula" is a computer program, this might
be tricker, depending on the program's complexity and what it's written in.

- LP

On 7/22/06, Kathy Dopp <kathy.dopp@gmail.com> wrote:
>
> On 7/21/06,
>
> > Message: 3
> > Date: Fri, 21 Jul 2006 11:30:35 -0700 (PDT)
> > From: "Edmund R. Kennedy" <ekennedyx@yahoo.com>
> > Subject: Re: [OVC-discuss] approximate solutions
> >
> > Hello Jerry:
> >
> > Actually the graphs and tables are still quite useful
> > for checking and cutting down orders of magnitude
> > errors.
> > While it's great to get precise solutions with
> > today's calculators and computers, it's much easier to
> > display how things relate to the variables with a
> > graphical approximation.
>
> Ed and Jerry,
>
> I love graphs, but there are four independent variables (election
> margin, total #vote counts, desired probability, and the assumed
> maximum rate of margin-shifting per machine) and one dependent
> variable - the vote count audit sample size. We could make graphs by
> holding three of the independent variables fixed and vary one of the
> independent variables for each graph, but you would end up with LOTS
> of graphs. The three variables with the fewest real life values for
> them that would be needed, would be assumed maximum margin
> shift/machine, probability and candidate margin, so taking candidate
> margins from 1% to say 15% and probabilities of say 90% to 98%, there
> could be 15*8 =120 charts that election officials could use to look up
> how many vote counts to select for audit if they have N vote counts in
> their county - assuming we give them only one option for max vote
> counts.
>
> I think that you are suggesting that we could simply do something
> like have 15 charts for the 15 margins of interest (assuming that all
> races in a county are audited with the same sample size determined by
> the race with the smallest margin -- I don't know enough yet to
> conclude that would be the case with optical scan ballots that you
> could sort to count, but I would assume that would have to be the best
> approach with stupid DRE paper rolls) each with nine curves on them
> for the nine probabilities they may want.
>
> To do a family of curves for a family of charts to make it easy to
> look up values for vote count auditing would require some
> decision-making re. the range of values to use to create charts and
> curves for.
>
> I agree with you that presenting a book of charts and/or tables for
> people to use to calculate vote count audit margins is a good idea
> providing the "family of curves" for each desired probability or
> candidate vote count margin don't overlap each other illegibly because
> then say 120 charts would be needed rather than 15 - but regardless,
> this is a big project that a computer would need to generate.
>
> So we still need a program or spreadsheet that will generate the
> charts for us, whether from an exact formula if we obtain one, or from
> an algorithm.
>
> A book of tables and charts may be more likely to be used than a
> spreadsheet that required trial and error or even a computer program
> that let users input the four independent vars and found the exact
> answer - is that what you're saying?
>
> Thanks.
>
> Kathy
>
> "Enlighten the people generally, and tyranny and oppressions of body
> and mind will vanish like evil spirits at the dawn of day," wrote
> Thomas Jefferson in 1816
> _______________________________________________
> OVC-discuss mailing list
> OVC-discuss@listman.sonic.net
> http://lists.sonic.net/mailman/listinfo/ovc-discuss
>

-- 
- Laird Popkin, cell: 917/453-0700

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Received on Mon Jul 31 23:17:06 2006

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