tag:blogger.com,1999:blog-264360878704809218.post7952608535561126839..comments2014-02-27T11:28:05.818-06:00Comments on Politely Avoiding Sophistry: What's Wrong with Risk Matrices?George Crewshttps://plus.google.com/102032704594804874665noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-264360878704809218.post-32167438437073296722013-05-15T17:48:39.488-05:002013-05-15T17:48:39.488-05:00I have a couple of issues with your assertion that...I have a couple of issues with your assertion that Cox's result depends only on ordinal properties.<br /><br />Risk is probability times consequence. And the exact same thing as consequence times probability. However, according to the Wikipedia article on ordinal arithmetic, ordinal multiplication is not communicative. So risk is not an ordinal number.<br /><br />As I mentioned, I don't have access to the original article since it's behind a pay-wall. So I am relying on Kailash Awati's "Eight to Late" blog post titled <i>Cox’s risk matrix theorem and its implications for project risk management</i>. (To anybody who hasn't read it, I highly recommend reading it. I link to it in my post above.) <br /><br />It states <i>Cox’s Second Lemma: if a risk matrix satisfies weak consistency and has at least two colours (green in lower left and red in upper right, if axes are oriented to depict increasing probability and impact), then no red cell can occur in the bottom row or left column of the matrix.</i> <br /><br />The proof of this Lemma (according to Awati) is based on the curved, hyperbolic shape of the iso-risk contours drawn on the risk matrix. However, as you can see from the figures above, these curved hyperbolas become straight, diagonal lines on a log-log scale.<br /><br />But as I made clear in my follow-up blog posting, this is not my big complaint with Cox's approach.George Crewshttps://www.blogger.com/profile/05795380097849494251noreply@blogger.comtag:blogger.com,1999:blog-264360878704809218.post-87661841064505027722013-05-15T16:41:17.997-05:002013-05-15T16:41:17.997-05:00Cox's results depend only on ordinal propertie...Cox's results depend only on ordinal properties, so log-transforming the axes does not affect them.Anonymousnoreply@blogger.com