A non-economic but still history-based way to estimate how much range voting would help humanity

We gave some
economic estimates
suggesting that by adopting range voting, countries could expect long-term improvement
in their annual economic growth rates of 1-10% additively, which, considering compounding,
would ultimately lead to massive advantages.

An entirely different (if crude) way to reach a similar conclusion is to check our
historical table of "wrong way elections."
Suppose out of 56 US presidential elections, 7 (i.e. one-eighth) have
been "wrong way." That rough estimate for the percentage of
wrong-way election under plurality voting is supported by the table.
(There are also probably even-larger bad indirect effects
caused by plurality voting such as numerous good candidates who do not even run
due to two-party domination, but we shall not even
attempt to estimate those losses here.)

So, with a good voting system, total "forward progress" in 8 elections would be:
"8 forward steps." With the poor plurality
voting system, we instead get "7 forward and 1 backward step, for
net forward progress 6 steps."
So countries with good voting systems can expect to "move forward" politically
33% faster.

Of course, even a "perfect" voting system which always gave the voters "what they wanted"
would not necessarily deliver the best results, since the voters have been known to
guess wrong. (For example, US President Warren G. Harding was elected in 1920 by one
of the largest-ever "landslides" but is one of the top choices among historians as "worst US
president ever.")
My personal estimate is the voters themselves make (what in hindsight was) the wrong choice
for about 25% of US presidents – you can make your own guess.
If so, a more realistic estimate would be that with good voting systems we
make 6 steps forward and 2 back (equals 4 forward) each 8 elections,
while with the plurality system it is 5 steps forwards and 3 back (equals 2 forward),
in which case
countries with good voting systems can expect to "move forward" politically
twice as quickly.

Try to translate that into economic improvement in your favorite manner.
It is not exactly clear what you'll get, but it is clear it is pretty substantial.
(Imagine living for a twice-as-long life. Think you'd accomplish more?)