# Re: approximate solutions

From: Edmund R. Kennedy <ekennedyx_at_yahoo_dot_com>
Date: Sat Jul 22 2006 - 14:09:20 CDT

Hello All:

First of all, have you considered triaxial charts, x
and y at 90 and z at 45 between them? They are a
little tricky to read sometimes but it is built into
most spread sheet programs. But, yes Kathy, I'm
thinking in terms of the intended audience, a college
educated but typically math-phobic humanties major who
are much more comfortable with graphs than equations.
(Full disclosure: Along with a BS I also have a BA.)
These days, most well constructed graphs also have the
parent equation(s) written on them so the graphs are
more like a teaching or checking tool. As long as you
can get the attention of the registrar of voters or
graphs and tables can be used to demonstrate there is
a possible problem, then your intended audience can
almost always find someone to actually do the number
crunching for them.

Thanks, Ed Kennedy

--- laird popkin <lairdp@gmail.com> wrote:

> 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
> > _______________________________________________
> OVC-discuss mailing list
> OVC-discuss@listman.sonic.net
> http://lists.sonic.net/mailman/listinfo/ovc-discuss
>

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Received on Mon Jul 31 23:17:06 2006

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