Hillary made 10000% returns over 10 months while the average senator makes 125% return over a year. 125% is still high but it's on a very different scale than the returns that Hillary made on the cattle-futures.
If you want to explain 125% returns than you can explain it with knowledge of upcoming legislation and those four factors.
On the other hand those factors don't make sense to explain how someone made 10000% returns by buying shorts when the market doubled over 10 months.
The statistical evidence is the study by Ziobrowski, Cheng, Boyd, and Ziobrowski of the stock portfolios of US Senators. They found that stocks held by Senators outperformed the market, with both purchase and sale significant events.
That sentence omits the interesting information that the senators underperformed the market in their sale decisions. That basically means the buying decision is often based on insider information and once most but not all of that information is priced in the senator sells the stock.
But I don’t know what drives the difference. [ between public perception of specific vs statistical results]
Most people approach such things socially rather than rationally. This is actually reasonable of them - there's no actual decision or prediction they're making based on it, so social cohesion and signalling is a fine motivation.
An important social distinction between the two types of evidence is that an individual case is directly about the person involved, with no prevarication or uncertainty if the hypothesis is accepted. If the cattle futures thing was bribery, then HC accepted bribe money. A statistical case has deniability for any individual even if the hypothesis is accepted. If the average senator buys stock on insider information, MY GUY might still be clean.
Thus, partisans who want to believe that a given individual is untainted are more motivated to deny the individual event than the statistical event. And if they do accept the event, they'll put a lot more importance on the individual than the statistical event.
Well, in the Hilary case my reason for favoring the "bribe" explanation is that presumably the person who first made the accusation was more familiar with the specifics of the situation than I am.
In the Senators case, anti-insider trading laws are written in such a way that they don't apply to Congressmen and their staff. So that makes that explanation more likely.
Already one of the best pragmatic statisticians, J. V. Stalin, knew that "One dead is tragedy, million dead is statistics".
There used to be important differences between stocks and futures (back when futures exchanges used open outcry) that (I think) enabled futures brokers to delay decisions about which customer got which trade price.
But I don’t know what drives the difference. I propose it as a question, not an answer.
Can you separate and bolden the question at the bottom?
People react to statistics very differently than they react to concrete examples, even though statistical generalities mean that there exist many concrete examples. Of course there are systematic differences between generalities and individual examples. For example, a concrete example might not be representative. Indeed, it probably is not representative for the very reason that it is at hand. But there are many other ways that people react differently that seem to me worthy of study.
I will compare two stories of political corruption, one statistical and one concrete that seem to me to have had rather different responses. It wouldn’t terribly surprise me if people had failed to believe one or the other. (Which would you expect?) But both of these stories were largely accepted as explained by corruption. Yet within the domain of corruption, the explanations of exactly how it was done were very different, practically disjoint.
The statistical evidence is the study by Ziobrowski, Cheng, Boyd, and Ziobrowski of the stock portfolios of US Senators. They found that stocks held by Senators outperformed the market, with both purchase and sale significant events. People generally accept this as corruption. People usually attribute the result to “insider trading,” and debate several specific theories: that Senators purchase based on their knowledge of upcoming legislation, or corporate information that leaks out in hearings; more corruptly, that stock ownership influences legislation, or that corporate insiders bribe Senators with corporate information.
The concrete example is that Hillary Clinton made a lot of money on cattle futures. This, too, is generally accepted as corruption. But I have never heard anyone put forward any of the four theories above to explain what happened there. Nor have I seen the specific explanation of the cattle futures trades put forward as an explanation of the Senate data. The popular explanation is that Clinton never made any bets based on any information, but that the trades were falsified after the fact to provide a paper trail to launder a bribe.
Of course, it is possible to reconcile the reactions. Perhaps people have a much higher prior on the first four hypotheses than on the fifth, so that they only consider it when the first four have been ruled out; though they don't discuss the process of ruling them out. Or, perhaps, it reflects important differences between stocks and commodity futures. But I think it is more likely that the reactions are inconsistent, one of them worse than the other. I think it likely that the different reactions reflect the concrete versus statistical natures of the two claims and other aspects of the context. Insider information is a standard answer provided by the context of an economics journal. More generally, statistical summaries sound definitive, so they demand to be explained, not to be rejected. While people are more willing to call bullshit on a story, even though a statistic is just a bunch of stories. Even in the context of already accusing large numbers of people of corruption. But I don’t know what drives the difference. I propose it as a question, not an answer.