Providing a sensible answer is dependent on arriving at a sensible interpretation of the question. I'll assume that it is aimed at understanding to what degree farming or non-farming lifestyles have had an influence on the selection of genes that you carry. I assume that "farming lifestyle" includes people who don't actually farm, but obtain food from farmers, one way or another.
On that basis, and assuming you are a typical inhabitant of a society that hasn't recently engaged in much hunting/gathering (maybe some fishing, but not dominant), I would say that about 1/30 of your ancestors were of a farming lifestyle. That is, if you trace back what the selective influences were on your ancestors, about 1/30 of it was selection for reproduction in a farming community. I get the 1/30 by dividing 300,000 years of homo sapiens into 10,000 years of agriculture.
I don't think the population sizes at different times, and collapse of the pedigree (some of your ancestors being the same people), make any difference. It might make a difference if the number of children per person varied, since each child is a new object for selection, but I think this may be rather constant until very recent times. And of course, the number of children who survive to reproduce themselves is close to two at all times. (The population has grown over time, but at nowhere near the rate it would if, say, three children per couple survived to reproduce themselves.)
Now, depending on how quick evolution can act, the fact that the 1/30 of the selection influence is the most recent 1/30 could be crucial.
Sorry, just read this response.
On the intuition question, my intuition was probably the other way because most of human history was non-farming, and because the vast majority of farmers (those born in the last millennium) weren't my ancestors.
I updated my model to account for an error - it's now a bit closer. 7.8 billion non-farmers to 6.4 billion farmers, and 4.9 billion exclusive farmers, but I still basically stand by the logic.
To respond to your question, why I didn't pick a fixed number of personal ancestors:
We have fewer recent ancestors, assuming 16 generations, we'd have around 20k to 50k ancestors at 1600. (2^16 - inbreeding). If we want to count these ancestors carefully, we should count back with an algorithm accounting for population size and exponentially increasing inbreeding.
We could also plausibly try to use this strategy to draw a more accurate number of ancestors from 1200-1600--- this might be a period where individual/geographical differences, or population constraints, play a significant role. If you're Icelandic, most of your ancestors in this period will still be from Iceland, but if you are Turkish, your ancestors from this period are more likely to extend from Britain to Japan. My model doesn't do this, because it sounds difficult, and because the numbers are negligible anyway- I just estimate that 0.1% to 1% of total humans born from 1200- today were my ancestors.
By around 1200 AD, it surely becomes impractical to rely on a personal family tree to track ancestry, because of the exponential growth in the number of ancestors. Beyond that point, your total potential ancestors (in the billions, without factoring in inbreeding) massively exceed the global population (in the 100s of millions). The limited population size becomes the constraint.
So an Italian might assume that they are descended from a significant portion (40%?) of Europe’s population in 1200 AD. By 800 AD, this would extend to a majority (60%?) of people living across Eurasia and Northern Africa. By the time we reach 500 BC to 1000 AD, it’s likely that most people from the major Old World civilizations and peripheries (where the bulk of the global population lived) were direct ancestors of people alive today. My numbers could be way off, but I think this is a better way of getting in the right ballpark than trying to trace back individual ancestry. I used these figures as a baseline. https://www.prb.org/articles/how-many-people-have-ever-lived-on-earth/
You're right that I don't account for major bottlenecks - my assumption is that they basically even out over time, and there's a constant 20-60% chance of humans born in each period not passing down ancestors to the modern day. If you wanted to refine this model you'd take into account more recent (e.g. Black Death) and less recent (Neolithic Y-chromosome bottleneck) bottlenecks.