Posts

Last updated 6/8/2020

I have graphed the number of new cases in seven-day increments versus the number of total cases. I use log-log on the axes because exponential curves show up as straight lines.  Each of the 4 countries plotted form a straight line on the graph suggesting exponential growth.  But in the cases of S. Korea and China the recent data fall dramatically off the exponential line suggesting their exponential growth has ceased.  All this assumes the data coming from China (and Iran) is correct. On the other hand, the US, and Italy are facing future unknown exponential growth.  Five other countries are graphed below with similar exponential growth = Germany, Iran, Spain, France, and UK.

Time can be thought of as moving along the colored lines/curves as the total number of cases increase. We should reach the end of the exponential growth of Coronavirus in the US (and Italy) when the data start to fall off the exponential lines downward (lower number of new cases). I will try to update the data each week. I have given the raw numbers below the graph.

I will update the graphs again in 7 days on June 15.

Raw data is from the following source: https://ourworldindata.org/coronavirus-source-data.

If you are unfamiliar with exponential growth, I suggest the following video: https://www.youtube.com/watch?v=54XLXg4fYsc&fbclid=IwAR1wY95Q6IWEKcmN0EYUh-3pSfUypr5tuJPp_bR5YaIHVcKUZYpSFpT7vyg&app=desktop

April 6
April 13
April 20
April 27
May 4 – added black line to show exponential growth
May 11
May 18
May 25
June 1
June 8

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Cases of Coronavirus in the following countries
China US Italy S. Korea
New Total New Total New Total New Total
wk 1 59 59
wk 2 59
wk 3 176 235 1 1
wk 4 2540 2775 5 5 0 0 3 4
wk 5 14436 17211 6 11 3 3 11 15
wk 6 22995 40206 1 12 0 3 12 27
wk 7 30412 70618 3 15 0 3 3 30
wk 8 6616 77234 20 35 129 132 732 762
wk 9 2900 80134 54 89 1557 1689 3450 4212
wk10 725 80859 465 554 5686 7375 3170 7382
wk11 161 81020 3220 3774 16605 23980 854 8236
wk12 629 81649 31432 35206 35158 59138 725 8961
wk13 814 82463 107819 143025 38551 97689 700 9661
wk14 485 82642 194610 337635 31259 128948 623 10284
wk15 567 83209 219936 557571 27415 156363 253 10537
wk16 608 83817 202116 759687 22609 178972 137 10674
wk17 382 84199 206223 965910 18703 197675 64 10738
wk18 52 83964 192131 1158041 13042 210717 63 10801
wk19 46 84010 171758 1329799 8353 219070 108 10909
wk20 44 84054 156958 1486757 6365 225435 156 11065
wk21 41 84095 156481 1643238 4423 229858 141 11206
wk22 52 84147 146953 1790191 3161 233019 297 11503
wk23 44 84191 152172 1942363 1979 234998 311 11814

Here are data for additional countries.

April 6
April 13
April 20
April 27
May 4
May 11

May 18
May 25
June 1
June 8
Cases of Coronavirus in the following countries
Germany Iran Spain France UK
New Total New Total New Total New Total New Total
wk 1
wk 2
wk 3
wk 4 3 3
wk 5 9 9 1 1 3 6 2 2
wk 6 4 13 1 2 5 11 2 4
wk 7 2 15 0 2 1 12 5 9
wk 8 0 15 43 43 0 2 0 12 4 13
wk 9 114 129 935 978 81 83 118 130 23 36
wk10 773 902 5588 6566 506 589 996 1126 237 273
wk11 3936 4838 7372 13938 7164 7753 4297 5423 1118 1391
wk12 19936 24774 7700 21638 20819 28572 10595 16018 4292 5683
wk13 32524 57298 16671 38309 50225 78797 24156 40174 13839 19522
wk14 38093 95391 19917 58226 51962 130759 30304 70478 28284 47806
wk15 27625 123016 13460 71686 35260 166019 24925 95403 36473 84279
wk16 18656 141672 10525 82211 29925 195944 17203 112606 35788 120067
wk17 13521 155193 8270 90481 18302 210895 11969 124575 32773 152840
wk18 7982 163175 6943 97424 8001 217466 6712 131287 33759 186599
wk19 6400 169575 10179 107603 6379 224390 7776 139063 32584 219183
wk20 5122 174697 12595 120198 3836 231606 3348 142411 24512 243695
wk21 3873 178570 15503 135701 3794 235400 2510 144921 15864 259559
wk22 3245 181815 15765 151466 4029 239429 6832 151753 15203 274762
wk23 2378 184193 20323 171789 2152 241550 2224 153977 11432 286194

Daniel Kahneman

Daniel Kahneman

I was struck by the vagaries of the lottery while watching a report on ABC News.  A wiley reporter asked several people if they would sell their Powerball ticket for $4 doubling the $2 they paid for it.  Each person refused the offer and seemed quite incredulous that the reporter would even ask.  I could not help thinking that it sounded like what Daniel Kahneman and Amos Tversky called loss aversion1.   More about that in a moment.

The behavior does seem capricious.  The odds were 1 out of 292 million to win $415 million2, but each person refused to sell claiming they might lose the millions.  Apparently it never occurred to them to sell the ticket and buy two more effectively doubling their chances of winning.  Nor did it make sense to them to sell the ticket and buy two additional tickets one with the same number they sold.  That may require having to split the winnings, but would that be onerous if they won especially considering the almost unimaginable odds against winning?

The magnitude of the chance to win is difficult to put into perspective, but it helps me to think in terms of toothpicks.   There are 250 toothpicks in a typical toothpick box and 73,000 give the requisite 292 million toothpicks needed to simulate the lottery odds.   Imagine only one toothpick in the 73,000 boxes is colored red.  If you could stack each box on top of one another, they would reach about 6,083 feet into the air – more than 800 feet higher than a mile.  Picture all those boxes being emptied, you being blindfolded and asked to scramble through the pile, and coming out with just one.  The odds of you picking the red toothpick are equivalent to you buying the winning lottery ticket.

But let’s get back to the original theme – loss aversion.   Daniel Kahneman is a psychologist, and normally psychologists are not in line to win Nobel Prizes in economics.  But he did in 2002 for his development of Prospect Theory, encompassing loss aversion, which attempts to explain the psychological impact of gains and loses.  He summarized his work in his best selling book Thinking, Fast and Slow3.   Prospect theory recognizes that humans are not completely rational.  They are risk averse and weigh losses much more heavily than gains (that is, loss aversion).

Let’s take for example a wager on the toss of a coin.  Tails you lose $100, heads you win $150.  Common sense tells us that winning more than we lose is a good bet.  After all, Vegas casinos make their livings on much less odds in their favor.  But most people will not take the bet.  They have a loss aversion.  Most require to win at least $200 before they accept the odds.

No need to get into much more detail on loss aversion, but I highly recommend Kahneman’s book if you crave more detail.   We can probably explain the unwillingness of some to sell their lottery tickets for double its’ worth because of loss aversion.  There must be a heuristic that imparts a need to keep that potential winning ticket even in the face of mind-boggling odds.  Perhaps loss aversion is hard-wired into our brains (that is, genetic).  Many of the genetic characteristics that make us human evolved within small hunter-gatherer tribes thousands of years ago4.

If our hunter ancestors were cutting up the carcass of an animal too large to carry, and a lion saw them and charged, it does not take too much imagination to believe they would take what they could and run rather then fight for the remainder.  They certainly would not be brain storming over what the rational decision would be.  You don’t get your genes passed on by taking time to formulate a rational path of action under do or die circumstances.

  1. Kahnerman, D. and Tversky, A. (1992) Advances in prospect theory: Cumulative representation of uncertainty: J. Risk and Uncertainty , 5, 297-323.
  2. The lump sum payout at $415 million is about $202 million after taxes which means paying for a $2 ticket is statistically a bad bet not that any of us would turn the money down.  And this does not consider the possibility of sharing the winnings with other winners.
  3. Kahneman, D. (2011) Thinking, Fast and Slow: Farrar, Straus and Giroux.
  4. Pinker, S. (2002) The Blank Slate: New York: Penguin.