I suppose that at this time of year, we're all thinking about how to greatly advance the funding aspect of gerontology research.
Well, my two cents might only be worth two pesos, but here it is.
I only briefly scanned through most messages in the Aubrey's IBG, Poll: Can we build it? and Billionaires, How to get through to them topics, since these topics have grown quite rapidly and I don't have much time at the moment.
A project I started in the last week of 2004 was to analyze the distribution of donations to the M Prize. I made no distinction about where the funds went: I simply used the numbers listed on the "donors" page. These are "lifetime" donation amounts, not the individual donations or the annual donation amounts. Analysis of those numbers may also be interesting, but it's not my focus here.
My intention was to analyze the "likelihood" that someone might donate a large sum, e.g. a million dollars, to the prize. What do I mean by likelihood? Well, comments in the Why Doesn't Kurzweil Really Donate to the MMP? topic got me to thinking about this.
Kurzweil donated 1,000$, less than half of what ImmInst regulars Reason and Kevin donated.
...
If Kurzweil really wants to live forever, wouldn't it be wiser for him to increase his donation by three, or four, orders of magnitude?
(my emphasis added)When you have money, you give only a little to each new cause. If said cause grows - i.e. shows it has responsible, sane, talented people at helm, then more later. I expect most of the early, wealthy donors to give more in the years ahead.
I began to think about this idea of growth. I am not suggesting that we not pursue efforts to win over an eccentric billionaire on the technical and vanity merits alone. But for me, I see my own path to blaze in increasing the "legitimacy" of the MMP. And this second quote highlights this path.
What sort of "growth" might signal to Kurzweil that the prize is worth putting in $100,000, or $1,000,000 of his own money?
What if the prize grew to $1 million? Would it be something as simple as the total money in the prize already? For that matter, would the "pledged" money--money not due for 25 years and not guaranteed to be collected--count towards some minimum size?
These questions are unanswerable by anyone but Kurzweil himself, but I'll venture a likely qualitative guess, and then risk a quantitative guess. I'll start with the issue of money in the bank, and worry about pledges in a few minutes.
Qualitatively, I think Kurzweil would be much more impressed if the M Prize could find thirty people willing to donate $10,000, than he would be by a single donor offering $1,000,000. Sure, it's only $300,000, a third of a million dollars, but those thirty donations speak of an underlying theme. One donation could be the work of an eccentric, but 30 donations? $10,000 pales compared to a million dollars, but it's still a very substantial investment of one's resources.
For that matter, I suspect that Kurzweil and other millionaires would be more impressed by a thousand people donating $100 each. That's about a third of the $300,000 I hypothesized from $10,000 donations, and about a tenth of the $1,000,000 from a single large donation. While the money is smaller, it speaks of large support from the community, indeed the creation of a meme. $100 isn't a sign of wealth, but it's far more than most people donate to the various cancer and heart disease charities, which are already well-established memes. It speaks of support from common folk like you and me (assuming that you're like me
).More importantly, 1,000 donations of $100 does not mean there are only 1,000 people who support the cause: many more support it who have been too shy or unable to donate. 1,000 donations of $100 speaks of a meme that has spread to perhaps tens of thousands of people.
If you don't agree with what I've said so far, then bail out now. Otherwise, I will press forward.
So, how do we quantify this? Statistics.
Disclaimer: Well, I really like statistics, but I've never studied it formally, except for an introductory probability and statistics course in college. I had to take the course, so I didn't study hard, didn't apply myself, and when all was said and done, I got a C in the class. Bear in mind that I almost always set the curve in my math and physics classes. In other words, I didn't really absorb that much from my statistics class, and I am, in effect, ignorant of it.
So, I've been spending the last three weeks reinventing centuries of statistical analysis techniques, with hours of painstaking number and thought experiments, often to find a quick one or two page summary of the same subject on Mathworld a few days later. But hey, the only way to truly understand some of these topics is to derive them on your own.
I put this disclaimer here to emphasize an important point: I went through several iterations of approaches to a quantitative analysis, trying to find the "best" one. I present here a brief summary of the early attempts, ending on a more detailed summary of where I eventually arrived.
Let me first start by saying something important. People's eyes will glaze over as I go into the math, so let me make this important point:
Surprisingly, two or three $10,000 donations will make a $100,000 or $1,000,000 donation more likely than getting a single $100,000 donation. Statistically anyway. While everyone seems focussed on getting more donations of $100,000, or $1,000,000, or $1,000,000,000, I'm quietly focussing on donations of $5,000 and $10,000. Ten or fifteen each of those (i.e. of $5,000 and $10,000 donations), and the $100,000 donations should start rolling in pretty quickly, followed by the $1,000,000. Of course, this is assuming that people don't stop donating $10 and $100; these donations add weight to the appearance that the longevity meme is catching fire.
I'll start with the basics. One million dollars is hard to quantify this early in the game, so I'll use more realistic numbers, and we'll extrapolate from there. I want a $100,000 donation to be roughly equivalent to $10,000 in $10 donations. A simple 3/4 power formula suffices. The following would then be of roughly equivalent value in describing how effective the longevity meme is, with respect to the M Prize:
10 donations of $100,000, totalling $1,000,000
56 donations of $10,000, totalling $560,000
316 donations of $1,000, totalling $316,000
1,778 donations of $100, totalling $177,800
10,000 donations of $10, totalling $100,000
Now 3/4 is a bit high: as far as emphasizing that a meme is spreading, 2/3 power would even suffice, and about a minimum is 1/2 power. Note that lower powers mean that we collect more money, so while the 3/4 power rule would be ideal, the bottom line is, we want money, so anything over 1/2 is fair game.
So we've got a power rule. Now what? Starting from here, we want a fairly "typical" distribution that we could associate with the meme. The first thing to notice is that we're quantifying this in terms of powers, which are best visualized by reducing things to orders of magnitude. Two that come to mind are the log-uniform distribution and the log-normal distribution. For ease, I will simply assume that we are speaking about the order of magnitude of a donation ($10 is 1, $1,000 is 3, $100,000 is 5, $31,622.78 is 4.5, $5,000 is about 3.699, etc.). In that case, we can analyze either a uniform distribution or a normal distribution.
For a uniform distribution, the "uniform" part refers to which power rule provides a flat distribution. The standard deviation is important as well: a small standard deviation means we're good at getting donations of a particular size (e.g. $100, or $1,000), but we're not getting the broad range that indicates that we're attracting people of varying means.
What about a normal distribution? I'll spare you the math, but I found that the normal distribution has an interesting property. The "power" rule I gave above doesn't matter. Whether we use a 1st power rule ($1,000,000 in $10 donations is just as important as $1,000,000 in $100,000 donations), a 0th power rule (a $10 donation is just as important as a $100,000 donation), or anything in between or outside this range, it doesn't matter: we'll still have a normal distribution.
However, what really affects things is the standard deviation, in orders of magnitude. Order 3 +/− 1 (a range of 2 to 4), equivalent to $1,000 ×/÷ 10 (a range of $100 to $10,000), gives us a different effect on total money from 3 +/− 2 (equivalent to the range $10 to $100,000).
So, where does the M Prize fit in? I started with the donations up to about Dec. 30, 2004, when the M Prize sum was listed as $105,948.40. Using the log(base10) of the donations, the mean and standard deviation came out to:
$117.18 ×/÷ 6.079, which gives a range of one standard deviation of $19.28 to $712.30. The mode and the median donation, for those who are interested, were both $100.00.
If you're not convinced that a logarithmic scale is appropriate, consider that the mean and standard deviation in the arithmetic scale are:
$623.23 +/− 2133.64. Notice that 0.3 standard deviations below the mean puts us in negative number territory. Also notice 135 donations are below the mean (specifically, between -0.29 and -0.01 standard deviations), 27 are 0 to 1 deviations above the mean, 3 are 1 to 2 deviations above the mean, and 5 are more than 2 standard deviations above.
# donations; deviations from mean
135; -0.29 to -0.01
28; 0 to 1
3; 1 to 2
5; 2 or more
On the other hand, for the log of the donation size, there are 21 donations less then one standard deviation below the mean, 76 donations between -1 and 0 deviations below the mean, 39 donations between 0 and 1 deviations above the mean, and 34 more than one standard deviation above the mean. Much more "normal", though still skewed.
# donations; deviations from mean
3; less than -2
18; -2 to -1
76; -1 to 0
39; 0 to 1
29; 1 to 2
5; 2 or more
(On a side note, if we add in Fisher's $100,000 donation, we see the arithmetic distribution become even more hopelessly skewed, while the logarithmic distribution remains very tame:
$1,204.38 +/− $7,870.26, a range of -$6,665.88 to $9,074.64
versus
$121.89 ×/÷ 6.499, a range of $18.75 to $792.21)
So, what's the bottom line? The distribution of donations is pretty close to a normal distribution, with some degree of skew which I will address shortly. The "mean" donation, by order of magnitude, is about $117, which is very close to the median and mode of $100. So for all those people who donated $100, but feel that their contribution isn't helping: believe me, it's helping!! You are the foundation of the Methuselah Mouse Prize. The members of the 300, whose donations will eventually bring the prize up into the millions without any help from millionaires, are the superstructure, the frame, if you will. But those who are donating anything within the $50 to $250 range (within half a standard deviation of the mean) are the foundation of this prize. Do not fret that the prize is growing far too slow compared to our dreams. What growth there is, is very significant and built not upon the backs of the $5,000 donors, nor even the $1,000 donors, many though they be, but upon the backs of the $100 donors.
The standard deviation is where we can see some room for improvement. It's very good to begin with: donations of $10 are about as common as donations of $1,000, and donations of $5 are about as common as donations of $2000 ($1800 to $2343.67). This prize is organic in nature, and those who withhold their $5 and $10 donations because they think that their donations are worthless, are missing the point that they are the counterpoint to the $1000 and $2000 donations. That's not to say that I'm promising that if you donate $10, someone else will automatically kick in $1,000. But those with more money to donate take a much longer look at what sort of "legitimacy", what sort of "crowd" has already put in their ante before them. Growing the standard deviation of the donation range gives us "ammunition" to go to people like Kurzweil and say, "See, this prize has gathered support from a broad range of people, with a broad range of means. We do not cater to merely the poor or the rich or the middle class, but to all people who care about life. This isn't just some publicity stunt to trick you into donating. This isn't a situation where we're after you for your money's sake. Your money would not be 'out of place', or 'conspicuous'. Quite the contrary, if we treat the donations as a statistical distibution, a donation of $100,000 or $1,000,000 at this point would not be unexpected." Compare that to the current distribution, where a donation of $1,000,000 would most certainly be out of place.
Would Kurzweil go for it? I don't know. But consider the following. First is a grouping, by order of magnitude, of the amount of money raised so far. Then a hypothetical example in which a donation of $100,000 would not be out of place, and then one in which a donation of $1,000,000 would not be out of place.
Current prize structure (as of Dec 30, 2004).
Mean ×/÷ Standard deviation:
$121.89 ×/÷ 6.499
Donation size; Number Donations; Money raised
$0.30-$3: 3; $4.00
$3-$30: 40; $715.86
$30-$300: 84; $9,957.34
$300-$3,000: 36; $40,923.70
$3,000-$30,000: 7; $54,347.50
$30,000-$300,000: 1 (optional); $100,000.00 (optional)
Total: 168; $205,948.4 (or $105,948.40)
Hypothetical scenario A
Mean ×/÷ Standard deviation:
$119.98 ×/÷ 9.432
Donation size; Number Donations; Money raised
$0.30-$3: 10; $17.50
$3-$30: 90; $1,203.01
$30-$300: 109; $13,575.78
$300-$3,000: 84; $105,643.92
$3,000-$30,000: 18; $153,600.00
$30,000-$300,000: 2; $150,000.00
Total: 313; $424,022.71
In this scenario, an eyeball of the trends indicates that a $100,000 donation would not be out of place (and a contrived mathematical sample of my own bears this out numerically), yet would still have a significant impact on the prize's cash value. By out of place, I mean that a millionaire putting in $100,000 would not feel like he's the only person going out on a limb, i.e. he (or she) would be in good company.
Hypothetical scenario B
Mean ×/÷ Standard deviation:
$136.10 ×/÷ 15.33
Donation size; Number Donations; Money raised
$0.30-$3: 59; $123.50
$3-$30: 203; $2,340.51
$30-$300: 228; $29,920.78
$300-$3,000: 177; $250,898.92
$3,000-$30,000: 90; $960,100.00
$30,000-$300,000: 15; $1,045,000.00
Total: 772; $2,288,260.21
In this scenario, a million dollar donation would not be out of place, and would indeed be "likely" if the distribution's characteristics hold. Notice that I've been expanding the standard deviation with each increasing scenario. Why? By expanding the standard deviation, I make a donation likely with a smaller ratio of funds already collected.
Right now, a "likely" large donation is $17,010.25; if you include Fisher's $100,000 donation, it only goes up to $21,277.89. Even if I allow a new single large donation to adjust the mean and the standard deviation, the the biggest donation that would be "likely" (50% probability of being one of the "samples" of the distribution) is $24,334.40. In other words, even with Michael Cooper's $25,000 donation and Fisher's $100,000 donation, the largest donation that might happen next is still less than $25,000.
And note that it took more than six times that much money to make that amount "likely" (more than eight times as much if we include Fisher's donation). The prize had to reach $105,000 to make $17,000 or $19,000 a "not unlikely" donation, and it took $205,000 to make $21,000 or $24,000 a "not unlikely" donation.
In scenario A, I've made $100,000 a "not unlikely" donation amount, with only $424,022.71 in the prize. This has effectively lowered the ratio of prize money needed to make a large donation "not unlikely". This was accomplished by raising the number of donations, the mean donation, and the standard deviation. By "encouraging" more people to donate $5 and $10, while at the same time factoring in that members of the 300 will bring in more donations of $1,000 and $5,000, I've raised the standard deviation. Of course there were more donations of $100, but some donations of $100 moved up to $200, and $200 donations moved up to $500, as people continued to donate in "2005". This pushed the mean up, in spite of the increase in $5 and $10 donations. Even a few extra $2.50 and $1.00 donations helped out.
In scenario B, I've lowered the ration further. Only $2,285,360.21 is in the prize, yet a donation of $1,000,000 is not unlikely. Here the ratio is almost 2:1, quite a bit lower than our current 6:1 ratio to get even a $100,000 donation.
I've further expanded the standard deviation. In scenario B, I assume that another fifty or so people have donated $5. You know, people who have not yet donated because they figured their $5 or $10 won't make a difference. If somehow we can bring them around, we can keep the standard deviation growing, even as the mean donation size goes up and up, as members of the 300 continue to fill in the fund with $2,000, $5,000, even $10,000 and $25,000. And by this point, a few wealthy philanthropists have put in $50,000 and $100,000 donations. Yet a million dollar donation would not be too much to ask of wealthy folks like Kurzweil or Paul Allen or any of the other wealthy philanthropists that have been mentioned.
One final note: I talk about this nebulous term, "not unlikely". While it's mathematically defined very well in my sample sets, applying this to real life must be taken with a grain of salt. For one thing, I think that the concept of making a $1,000,000 donation "not unlikely" could be applied not to the entire set of millionaire and billionaire philanthropists, but to each individual philanthropist whom we could present with a report that includes details of the SENS project, as well as a statistical analysis similar to the one I've outlined. In other words, if we could get three or four wealthy philanthropists to listen to us, we might not even need a million dollars to get one to step forward with a million dollars.
Another thing I have not factored in is the long-term value, based on the 25-year pledges. This too allows us to raise our "cash value".
However, if we're going to be honest to our wealthy philanthropist audience, we must A) discount the future, and B) make a measurement of the integrity of the members of the 300.
A is simple: we discount the remaining money due by the members of the 300, by some excessive discount rate, perhaps 7%.
B is also simple: we show current history of 300 membership, in terms of fulfillment of obligations. This is hard right now, since so few of the 300 members have been members for a year. However, a year from now, we'll have 30 members of the 300 that we can get data for, and as long as all 30 of us have donated at least $1,000 by our first anniversary dates, and $2,000 by our second anniversary dates, then we should be able to make the case that our discounted figures are accurate. By the time we have three years worth of data, with hopefully well over 100 members of the 300, we should have no problem attracting multiple one million dollar donations. However, getting that first one will be tricky.
I promised I'd get to that "skew" thing, but alas, I'm out of time. I'll pick up on that theme in the next few days.
