<div dir="ltr"><div class="gmail_default" style="font-family:comic sans ms,sans-serif;font-size:small;color:rgb(0,0,0)"><span class="im"><pre cols="72">We should have a way of dealing with those cases where foul play is un likely but possible. <br>We might estimate perhaps 10 percent chance Scalia was slain, ja?<br><br></pre><pre cols="72">On the basis of no evidence at all? This is very far from scientific thinking.<br><br></pre><pre cols="72">bill w<br></pre></span></div></div><div class="gmail_extra"><br><div class="gmail_quote">On Thu, Feb 18, 2016 at 5:28 PM, Anders Sandberg <span dir="ltr"><<a href="mailto:anders@aleph.se" target="_blank">anders@aleph.se</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div bgcolor="#FFFFFF" text="#000000"><span class="">
On 2016-02-18 15:35, spike wrote:<br>
<blockquote type="cite">
... By the way, does anybody have a good long-term database of
historical assassinations? <br>
<pre cols="72">--
Anders
</pre>
<pre cols="72">We should have a way of dealing with those cases where foul play is un likely but possible. We might estimate perhaps 10 percent chance Scalia was slain, ja?</pre>
</blockquote>
<br></span>
Actually, way lower. Think of it like this: the murder rate of the
US is about 4 per 100,000, or <span>a
probability of 0.00004. <br>
<br>
There are no doubt some murders that are successfully hidden as
natural; if we assume for every discovered murder there is a
hidden one we are likely extremely paranoid, but that brings up
the probability to </span><span>0.00008.
<br>
<br>
Now, assassinations are actually fairly rare: most murder is of
non-prominent persons. Even there, judges are uncommon (in the
data in </span>Snitch, T. H. (1982). Terrorism and political
assassinations: A transnational assessment, 1968-80. <i>The Annals
of the American Academy of Political and Social Science</i>,
463(1), 54-68. only 3% of successful assassinations involved
judges). So thinking a particular judge's death is due to foul play
without any supporting evidence should lower the probability of the
statement being true by quite a lot - a very rough assassination
rate (assassinations/deaths) I estimated using Wikipedia statistics
is 7.8e-4. A lot of those deaths were murders, so let's be
charitable and say a factor of 1e-3. That makes a probability of
8e-8. <br>
<br>
So, the ultra-paranoid prior for Scalia being assassinated is a
probability of 8e-8. <br>
<br>
Now, if you started to get positive evidence that prior would be
multiplied by Bayes factors of the form
P(evidence|assassination)/(P(evidence|assassination)P(assassination)
+ P(evidence|no assassination)P(no assassination), which is roughly,
since assassinations are rare,
P(evidence|assassination)/P(evidence|no assassination). For example,
lack of autopsy is pretty likely in either case, so the Bayes factor
is only slightly larger than 1. Seeing ninjas disappear from the
scene produces a big factor, since they rarely show up when people
die for non-assassination reasons. Not seeing ninjas (because maybe
they are invisible like all really good ninjas!) produces a Bayes
factor of 1: you would expect that in either case. <br>
<br>
So, can anybody scrounge up enough Bayes factors to get the prior up
to 0.1?<span class=""><br>
<br>
<pre cols="72">--
Anders Sandberg
Future of Humanity Institute
Oxford Martin School
Oxford University</pre>
</span></div>
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