Robert Carroll wrote:Brian,
The key here is to interpret "significantly more likely" correctly in the context. Is 100% significantly more than 40%? You're viewing this as a question with a fixed answer. In other words, in your interpretation, "Is 100% significantly more than 40%?" can be answered affirmatively or negatively without a context. You think it's clear that 100% is significantly more than 40%. It's not. Let me explain by returning to the rather extreme situation you discussed earlier, where the disparity in percentages was even worse.
So, in that extreme situation, 2 people are pro-tariff and each of those 2 people bases his/her vote on tariffs. 51 people are anti-tariff, and 10 of those people (roughly 20%, as you point out) base their votes on tariffs. In this case, it is possible for 100% of the pro-tariff people to base their votes on tariffs and only 20% of the anti-tariff people to base their votes on tariffs, yet a politician would not have to worry about this - ignoring the pro-tariff minority would be perfectly acceptable, from a vote-getting perspective. This hypothetical is supposed to be a situation in which the supporters of tariffs are significantly more likely to vote based on tariffs than opponents of tariffs. Thus, this is supposed to be a situation that matches the negation of answer choice (A). According to the Assumption Negation technique, this situation should destroy the argument, yet it doesn't.
The flaw in the reasoning above is as follows. For this situation to be an example of the negation of answer choice (A), it would have to be a situation where significantly more of the pro-tariff people base their votes on tariffs than the anti-tariff people base THEIR votes on tariffs. The question then is "Is 100% significantly more than 20%?" The correct answer is not "Yes, of course 100% is significantly more than 20%" but instead "It depends." Look at the case here - 100% of 2 people is not more than 20% of 51 people. So, in this very case, 100% is not significantly more than 20%, because 100% of 2 people is not more people than 20% of 51 people. Comparing percentages is senseless here - we need to compare numbers. For the likelihood to be significant, it would have to be a percentage so much higher that the resulting part of the pro-tariff population is higher than the resulting part of the anti-tariff population. The key is what "significant" means. If pro-tariff people are sufficiently few in number, even a portion of that population as high as 100% fails to be significant. Thus, the "2 pro vs 51 anti" hypothetical is inapt. Any other such hypothetical that does not result in more votes on the pro side than the anti side will have a similar defect, so the flaw extends to all such examples.
This means the negation of answer choice (A) does destroy the argument, proving it was an assumption necessary for the argument.
Robert Carroll
Robert, thank you for responding.
So from all that you've said above the big thing I'm getting is the meaning of the word "significant". Basically, you're saying that the use of the word "significant" FORCES the absolute number of pro-tariff people likely to base their vote on the politician's stance on tariffs to be higher than the number of anti-tariff people likely to base their vote on that same issue. Is this an accurate summary of your explanation?
If so, and if the key to getting this answer right is an understanding of the word "significant" that allows you to make a determination out of thin air to make a statement about any type of absolute numbers, then I again have to say this this explanation is unsatisfactory.
Essentially, if we interpret "significant" like you're saying we can/should, then a negated answer choice A will read something like "the absolute number of pro-tariff people voting on the basis of tariffs is higher than the absolutely number of anti-tariff people voting on the basis of tariffs". That, to me, seems like an astronomical jump from what it actually says. Your definition of the word seems arbitrarily established to eliminate any possible world where the letter of the question would allow for A to be negated and the argument still stand (like the middle paragraph in your post). It seems to go against the conventional understanding of what "significantly more likely" means.
But, to be fair, I highly doubt that I have studied the LSAT as long as you have or have seen anywhere near as many questions as you have. So if you, or anyone else at Powerscore, could show me some examples of where the test forces you to interpret "significantly more likely" in the way you do above, I would really appreciate it. Otherwise, at this point, if I miss a question like this that I believe is fundamentally flawed, then I guess I'll just have to live with it.
Thank you all for your help and patience.