GDP measures essentially how good we are at making widgets - and while widgets are useful, it is a very weak and indirect measure of welfare. For example UK GDP per capita doubled between 1975 and 2007 - and people's quality of life indeed improved - but it would be extremely difficult to argue that this improvement was "doubling", and that the gap between 2007's and 1975's quality of life is greater than between 1975's and hunter-gatherer times.

It's not essential to this post, but my very quick theory is that we overestimate GDP thanks to economic equivalent of Amdahl's Law - if someone's optimal consumption mix consisted of 9 units of widgets and 1 unit of personalized services - and their purchasing power increased so now they can acquire 100x as many widgets, but still the same number of services as before - amount of the mix they can purchase increased only 9x, not 90x you'd get by weighted average of original consumption levels (and they spend 92% of their purchasing power on services now). The least scalable factor - whichever it is - will be the bottleneck.

If we're unhappy with GDP there are alternative measures like HDI, but they're highly artificial. It would be very easy to construct completely different measures which would "feel" about as right.

Fortunately there exists a very natural measure of welfare, which I haven't seen used before in this context - preference utilitarian lotteries. Would you rather live in 1700, or take a 50% chance of living in 2010 or 700? Make a list of such bets, assign numbers coherent with bet values (with 100 for highest and 0 for your lowest value) and you're done! By averaging many people's estimates we can hopefully reduce the noise, and get some pretty reasonable welfare estimates.

And now disclaimer time. This approach has countless problems, here are just a few but I'm sure you can think about more.

• Probabilities are difficult - People are really bad at intuiting about a difference between 1% chance of something vs 3% of something, even though it will count for three times as much in results. We can mostly work around this problem by not comparing extremes, but instead sorting situations by desirability, and only comparing nth situation, with p chance of n+1st vs (1-p) chance of (n-1)st. Such probabilities will usually be in comfortable medium range.
• Risk aversion - you prefer certainty of moderate outcome to change of getting either good or bad outcome. It tends to overestimate past welfare.
• Status quo bias - you prefer situations closer to your current even if there's no actual welfare difference. It tends to underestimate past welfare, perhaps balancing risk aversion.
• Knowledge problem - now how much do you really know about life in Industrial Revolution time Britain, let alone ancient Sumer? Even professional historians have problems with that, and unfortunately we might all be biased the same way negating some benefit of averaging out estimates.
• Values problem - you might find some civilizations more repulsive and others less because of your modern values, even if their welfare is really not that different. It can be infanticide (extremely common historically), slavery, racial discrimination, human sacrifice, particular religion or political system etc.
• Hindsight - reverse of knowledge problem - life in 1345 Florence was nowhere near as bad as our hindsight estimates would make it be.
• Representative sampling - life of exactly whom? In many times a random person born wouldn't survive to adulthood - yet it seems unreasonable to include those. Let's say we focus on a healthy adult somewhere near median social status and income.

I tried to think about such series of bets and my results are:

• Western Europe 2010 CE - 100
• Western Europe 1980 CE - 97
• Western Europe 1950 CE - 91
• Western Europe 1900 CE - 65
• Western Europe 1800 CE - 26
• Western Europe 1700 CE - 16
• Western Europe 1500 CE - 10
• High Middle Ages Europe (1250 CE) - 7.6
• Early Middle Ages Europe (700 CE) - 6.4
• Roman Empire around 100 CE - 7.1
• Mediterranean World 500 BCE - 7.0
• Neolithic Middle East (5000 BCE) - 1.6
• Paleolithic anywhere (20000 BCE) - 0

This seems far more reasonable than GDP's illusion of exponentially accelerating progress.

I used this Ruby code to convert bets to values on scale of 0 to 100 (bets ordered by preference, not chronologically):

def linearize_ratios(*ratios)
  diffs = ratios.inject([1.0]){|d,r| d + [d[-1] * r / (1-r)]}
  scale = diffs.inject{|a,b|a+b}
  diffs.inject([100]){|v,d| v + [v[-1] - 100.0 * d / scale]}
end
p linearize_ratios(0.7, 0.8, 0.6, 0.2, 0.4, 0.25, 0.2, 0.1, 0.9, 0.9, 0.25)