You are posing some quite interesting questions which generally have not addressed by much of anybody in a careful way. However, some of the comments I have heard make the following points: This type of ballot does cause problems (as do other types for this matter) and that has been documented in a number of places besides Palm Beach (places where, as near as I can tell, that Democrats nor Republicans have challenged) so there is probably some difficulty with this sample of 2nd graders (100% is a bit too high). Some possibilities are the ballot used in Palm Beach is, in some fashion, different than used by the 2nd graders. The instructions given to the second graders is different than that given to the Palm Beach folk. Second graders tend to follow instructions more carefully than us older folk. The second graders' ballots were hand-scored under different criteria. And so on. Largeness may not be relevant. But representative is a good question.
However, on the other hand, if one were to say that this is a bit of Republician statistical proproganda, it is not much worse than something others might say is Demcoratic statistical propogranda. In both cases, what we have are what one might term analyses which falter on the concept of representations. But this is where statistics always falters. And statistical analyses in the social sciences are, in my opinion, inherently problematic (but I have mathematical suspicions about the natural sciences - smile). Anyway this analysis, as others favoring other views, does seem to say that, as one colleague has remarked, the Palm Beach fiasco (and he generously includes both, I think rightly, Democrats and Republicans) is not quite as it has been painted by whoever. That is perhaps useful and something that might definitely be considered by some of our more entrenched comrades, but it is tenuous at best.
But all this raises some interesting questions as to just what statistics is doing in the social sciences, and even more interesting is how are we to interpret the numbers so generously generated.
Oh, thank you for your polite reply to Michael. In my opinion, he certainly didn't deserve it.
>Maybe I didn't state the case clearly enough. The question I >proposed is whether the sample of the 2nd grade class was >representative and large enough to say whether it was reasonable to >believe that the West Palm Beach ballot design was bad. How large a >sample would be good enough? What makes a good representative >sample? Can we use stories like this to get kids to think about >these issues? > >-Jody > > > >At 4:01 PM -0500 11/15/00, Michael Paul Goldenberg wrote: >>I'm sorry, but Jody's post is itself a political statement. Why is it >>significant that the 2nd graders could do the punch cards so well? Does that >>say something about math? Or is it a left-handed slap at the intelligence, >>competence, and/or eyesight of the elderly Jewish and African-American >>voters who screwed up? Please don't tell me that your mention of that was >>just a neutral comment. And who decides, exactly, what is and is not >>on-point? You? Greg? Me? Victor? A machine? >> >>Michael Paul Goldenberg >>Washtenaw Technical Middle College >>LA 230K >>Ann Arbor, MI 48106 >>(o)734 477-8560 (h) 734 482-0497 >>firstname.lastname@example.org email@example.com >>http://courses.wccnet.org/~mikegold/ >>"Truth is a mobile army of metaphors." Nietzsche >> >> > -----Original Message----- >> > From: Jody Underwood [mailto://firstname.lastname@example.org] >> > Sent: Wednesday, November 15, 2000 10:50 AM >> > To: karen jones; email@example.com >> > Cc: Greg Goodknight; Gerald Von Korff; Math Forum >> > Subject: Re: Count all the votes >> > >> > >> > I'd like to follow up on what Karen Jones-Budd said -- this isn't a >> > political forum. Since there's so much interest in having political >> > flame wars, perhaps you should split off and create >> > math-teach.politics. >> > >> > I'd like to bring back Annie Fetter's post -- for people to share >> > with Math Forum folks and with this list how they have used voting in >> > their math classes. I was looking forward to seeing the responses to >> > this, but the responses were mostly political! >> > >> > The only thing that came close was the "Count all the votes" post by >> > Gerald Von Korff. However, it fell short because it didn't talk >> > about the math involved, and how we can get our students interested >> > in this very unique phenomenon. Isn't there a way we can take >> > advantage of this situation? >> > >> > I've got a couple of relevant stories. Did you hear about the 4th >> > grade class who were asked to vote for Gore on ballots that were just >> > like the ones used in West Palm Beach, FL? 100% of them were able to >> > successfully vote for Gore in less than 1 minute. Here's the usenet >> > posting about it: >> > >> > >> >> >>Or this story on 2nd graders voting for their favorite Disney >>character using that ballot: >> >> >> >>While these are interesting stories, are they good samples? What can >>we do with them with our students? >> >>Another lesson comes to mind on modeling what happens when any 2 >>people count a large amount of cards with more than 2 categories in >>them -- will it come out the same both times? >> >>Can we get anything other than statistics and probability examples? >> >>Greg Goodknight's post was trying to get at some issues, and though >>they weren't strictly about math, they were about testing and >>reliability. I would be very interested to see some answers to his >>questions. Does anyone have references to the tests that have been >>done on the ballot counting and the machines? >> >>(Btw, my experience with punch cards tells me that the problem is not >>that the punch hole did not come out completely, but that the card >>reader reads more than one card at once. These old machines need to >>be tuned on a regular basis. But I didn't hear that reason from the >>media. So much for believing what the media tells you about >>something you know. But I digress. (But I'm not flaming another >>poster!) ) >> >>Here's to talking about math and teaching math. Can we get on track? >> >>-Jody >> >>-- >>Jody S. Underwood, Ph.D. >>Educational Technologist & Research Associate 610-544-3644 x213 >>The Math Forum 800-756-7823 >>101 South Chester Road, Suite 400 610-544-1358 (fax) >>P.O. Box 156 firstname.lastname@example.org >>Swarthmore, PA 19081-0156 http://mathforum.com/~jody/