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are in the jhanas. The pleasant sensations can be so strong to eliminate your painful sensations. You enter the jhanas from the pleasant experiences exploding into a state of ecstasy where you no longer “feel” any of your senses. –9 Jhanas, Dhamma Wiki(“9 Jhanas,” n.d.) There are 8 (or 9, depending on who you ask) “levels” of Jhanas, and the above is describing only the 1st of them! The higher the Jhana, the more refined the bliss becomes, and the more detached the state is from the common referents of our everyday human experience. Ultra-bliss does not look at all like sensual pleasure or excitement, but more like information-theoretically optimal configurations of resonant waves of consciousness with little to no intentional content (c.f., semantically neutral energy(Johnson 2018)). I know this sounds weird, but it’s what is reported. “Streamlines from the insula to the cortex” – the insula (in red) is an area of the brain intimately implicated in the super-bliss that sometimes precedes temporal lobe epilepsy(Ghaziri et al. 2017). Another example I’ll provide about ultra-bliss concerns temporal lobe epilepsy, which in a minority of sufferers gives rise to extraordinarily intense states of pleasure, or pain, or both. Such experiences can result in Geschwind syndrome, a condition characterized by hypergraphia (writing non-stop), hyper-religiosity, and a generally intensified mental and emotional life. No doubt, any experience that hits the valence scale at one of its extremes is usually interpreted as other-worldly and paranormal (which gives rise to the question of whether valence is a spiritual phenomenon or the other way around(Emilsson 2017b)). Famously, Dostoevsky(Baumann et al. 2005) seems to have experienced temporal lobe seizures, and this ultimately informed his worldview and literary work in profound ways. Here is how he describes them: “A happiness unthinkable in the normal state and unimaginable for anyone who hasn’t experienced it [. . . ] I am then in perfect harmony with myself and the entire universe.” – From a letter to his friend Nikolai Strakhov. “I feel entirely in harmony with myself and the whole world, and this feeling is so strong and so delightful that for a few seconds of such bliss one would gladly give up 10 years of one’s life, if not one’s whole life. [. . . ] You all, healthy people, can’t imagine the happiness which we epileptics feel during the second before our fit. . . I don’t know if this felicity lasts for seconds, hours or months, but believe me, I would not exchange it for all the joys that life may bring.” – From the character Prince Myshkin in Dostoevsky’s novel, The Idiot, which he likely used to voice his own experiences. Dostoevsky is far from the only person reporting these kinds of experiences from epilepsy: As Picard [a scientist investigating seizures] cajoled her patients to speak up about their ecstatic seizures, she found that their sensations could be characterised using three broad categories of feelings(Picard and Craig 2009). The first was heightened self-awareness. For example, a

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53-year-old female teacher told Picard: “During the seizure it is as if I were very, very conscious, more aware, and the sensations, everything seems bigger, overwhelming me.” The second was a sense of physical well-being. A 37-year-old man described it as “a sensation of velvet, as if I were sheltered from anything negative.” The third was intense positive emotions, best articulated by a 64-year-old woman: “The immense joy that fills me is above physical sensations. It is a feeling of total presence, an absolute integration of myself, a feeling of unbelievable harmony of my whole body and myself with life, with the world, with the ‘All,’” she said. – From “Fits of Rapture,” New Scientist(Hines 2014) All in all, these examples illustrate the fact that blissful states can be deeper, richer, more intense, more conscious, and qualitatively superior to the normal everyday range of human emotion. Now, how about the negative side? Logarithmic Pain Scales: Stings, Peppers, and Cluster Headaches “The difference between 6 and 10 on the pain scale is an exponential difference. Believe it or not.” – Insufferable Indifference, by Neil E. Clement (who experiences chronic pain ranging between 6/10 to 10/10, depending on the day) Three pain-scale examples that illustrate the non-linearity of pain are: (1) the Schmidt sting pain index, (2) the Scoville scale, and (3) the KIP scale: Schmidt’s Sting Pain Index. Justin O. Schmidt stung himself with over 80 species of insects of the Hymenoptera order, and rated the ensuing pain on a 4-point-scale. About the scale, he had to say the following: 4:28 – Justin Schmidt: The harvester ant is what got the sting pain scale going in the first place. I had been stung by honeybees, yellow jackets, paper wasps, etc. the garden variety stuff, that you get bitten by various beetles and things. I went down to Georgia, which has the Eastern-most extension of the harvester ant. I got stung and I said “Wooooow! This is DIFFERENT!” You know? I thought I knew everything there was about insect stings, I was just this dumb little kid. And I realized “Wait a minute! There is something different going on here,” and that’s what got me to do the comparative analysis. Is this unique to harvester ants? Or are there others that are like that. It turns out while the answer is, now we know much later – it’s unique! [unique type of pain]. […] 7:09 – Justin Schmidt: I didn’t really want to go out and get stung for fun. I was this desperate graduate student trying to get a thesis, so I could get out and get a real job, and stop being a student eventually. And I realized that, oh, we can measure toxicity, you know, the killing power of something, but we can’t measure pain. . . ouch, that one hurts, and that one hurts, and ouch that one over there also hurts. . . but I can’t put that on a computer program and mathematically analyze what it

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text:
means for the pain of the insect. So I said, aha! We need a pain scale. A computer can analyze one, two, three, and four, but it can’t analyze “ouch!” So I decided that I had to make a pain scale, with the harvester ant (cutting to the chase) was a 3. Honey bees was a 2. And I kind of tell people that each number is like 10 equivalent of the number before. So 10 honey bee stings are equal to 1 harvester ant sting, and 10 harvester ant stings would equal one bullet ant sting. […]11:50 – Interviewer : When I finally worked up the courage to [put the Tarantula Hawk on my arm and] take this sting. The sting of that insect was electric in nature. I’ve been shocked before, by accidentally taking a zap from an electrical cord. This was that times 10. And it put me on the ground. My arm seized up from muscle contraction. And it was probably the worst 5 minutes of my life at that point. Justin Schmidt: Yeah, that’s exactly what I call electrifying. I say, imagine you are walking along in Arizona, and there is a wind storm, and the power line above snaps the wire, and it hits you, of course that hasn’t happened to me, but that’s what you imagine it feels like. Because it’s absolutely electrifying, I call it debilitating because you want to be macho, “ah I’m tough, I can do this!” Now you can’t! So I tell people lay down and SCREAM! Right? Interviewer : That’s what I did! And Mark would be like, this famous “Coyote, are you ok? Are you ok?” Justin Schmidt: No, I’m not ok! Interviewer : And it was very hard to try to compose myself to be like, alright, describe what is happening to your body right now. Because your mind goes into this state that is like blank emptiness. And all you can focus on is the fact that there’s radiating pain coming out of your arm. Justin Schmidt: That’s why you scream, because now you’re focusing on something else. In addition to the pain, you’re focusing on “AAAAAAHHHHH!!!” [screams loudly]. Takes a little bit of the juice off of the pain, so maybe you lower it down to a three for as long as you can yell. And I can yell for a pretty long time when I’m stung by a tarantula hawk. – Origin of STINGS!, interview of Justin O. Schmidt(“Origin of STINGS!” 2017). If we take Justin’s word for it, a sting that scores a 4 on his pain scale is about 1,000 times more painful than a sting that scores a 1 on his scale. Accordingly, Christopher Starr (who replicated the scale(“Starr Sting Pain Scale” 2020)), stated that any sting that scores a 4 is “traumatically painful”(Starr 1985). Finally, since the scale is restricted to stings of insects of the Hymenoptera order, it remains possible that there are stings whose pain would be

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rated even higher than 4. A 5 on the sting pain index might perhaps be experienced with the stings of the box jellyfish that produces Irukandji syndrome, and the bite of the giant desert centipede. Needless to say, these are to be avoided. Moving on… Examples of peppers on the Scoville Scale.(“Scoville Scale” 2020) (2) The Scoville scale measures how spicy different chili peppers and hot sauces are. It is calculated by diluting the pepper/sauce in water until it is no longer possible to detect any spice in it. The number that is associated with the pepper or sauce is the ratio of water-tosauce that makes it just barely possible to taste the spice. Now, this is of course not itself a pain scale. I would nonetheless anticipate that taking the log of the Scoville units of a dish might be a good approximation for the reported pain it delivers. In particular, people note that there are several qualitative jumps in the type and nature of the pain one experiences when eating hot sauces of different strengths (e.g., “Fuck you Sean! [. . . ] That was a leap, Sean, that was a LEAP!” – Ken Jeong right after getting to the 135,000 Scoville units sauce in the Youtube series Hot Ones(“Ken Jeong Performs a Physical While Eating Spicy Wings | Hot Ones” 2019)). Amazon reviews of ultra-hot sauces can be mined for phenomenological information concerning intense pain, and the general impression one gets after reading such reviews is that indeed there is a sort of exponential range of possible pain values: Previous Next I know it may be fun to trivialize this kind of pain, but different people react differently to it (probably following a long-tail too!). For some people who are very sensitive to heat pain, very hot sauce can be legitimately traumatizing. Hence I advise against having ultra-spicy sauces around your house. The novelty value is not worth the probability of a regrettable accident, as exemplified in some of the Amazon reviews above (e.g., a house guest assuming that your “Da’Bomb – Beyond Insanity” bottle in the fridge can’t possibly be that hot. . . and ending up in the ER and with PTSD). I should add that media that is widely consumed about extreme hot sauce (e.g., the Hot Ones mentioned above and numerous stunt Youtube channels) may seem fun on the surface, but what doesn’t make the cut and is left in the editing room is probably not very palatable at all. From an interview with Sean Evans, Hot Ones host: “Has anyone thrown up doing it?” Interviewer : “Yeah, we’ve run the gamut. We’ve had people spit in buckets, half-pass out, sleep in the green room afterwards, etc.”(“Sean Evans of ’Hot Ones’ –Best/Worst Guests, Publicists, Khaled, Etc –Jim Norton & Sam Roberts” 2019). T.J. Miller, when asked about what advice he would give to the show while eating ultra-spicy wings, responded: “Don’t do this. Don’t do this again. End the show. Stop doing the

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text:
show. That’s my advice. This is very hot. This is painful. There’s a problem here.”(“T.j. Miller Talks Deadpool, Hecklers, and Relationship Advice While Eating Spicy Wings | Hot Ones” 2016) Trigeminal Neuralgia pain scale – a condition similarly painful to Cluster Headaches. Reprinted with permission from www.facebook.com/endTrigeminalNeuralgia. Finally, we come to the “KIP scale,” which is used to rate Cluster Headaches, one of the most painful conditions that people endure: KIP-0 No pain, life is beautiful. KIP-1 Very minor, shadows come and go. Life is still beautiful. KIP-2 More persistent shadows. KIP-3 Shadows are getting constant but can be dealt with. KIP-4 Starting to get bad, want to be left alone. KIP-5 Still not a “pacer” but need space. KIP-6 Wake up grumbling, curse a bit, but can get back to sleep without “dancing.” KIP-7 Wake up, sleep not an option, take the beast for a walk and finally fall into bed exhausted. KIP-8 Time to scream, yell, curse, head bang, rock, whatever works. KIP-9 The “Why me?” syndrome starts to set in. KIP-10 Major pain, screaming, head banging, ER trip. Depressed. Suicidal. The duration factor is multiplied by the intensity factor, which uses the KIP scale in an exponential way - a KIP 10 is not just twice as bad as a KIP 5, it’s ten times as intense. - Keeping Track by Cluster Busters(“Busting Protocol — Keeping Track” 2020). As seen above, the KIP scale is acknowledged by its creator and users to be logarithmic in nature. In summary, we see that pleasure comes in various grades and that peak experiences such as those induced by psychedelics, meditation, and temporal lobe seizures seem to be orders of magnitude more energetic and better than everyday sober states. Likewise, we see that across several categories of pain, people report being surprised by the leaps in both quality and intensity that are possible. More so, at least in the case of the Schmidt Index and the Kip Scale, the creators of the scale were explicit that it was a logarithmic mapping of the actual level of sensation. While we do not have enough evidence (and conceptual clarity) to assert that the intensity of pain and pleasure does grow exponentially, the information presented so far does suggest that the valence of experiences follows a long-tail distribution. Deference-type Approaches for Experience Ranking The above considerations underscore the importance of coming up with a pleasure-pain scale that tries to take into account the non-linearity and non-normality of valence ratings. One idea we came up with was a “deference”-type approach, where we ask open-ended questions about people’s best and worst experiences and have them rank them against each other. Although locally the data would be very sparse, the idea was that there might be methods to integrate the collective patterns of deference into an approximate scale. If extended to populations of people who are known to have experienced extremes of valence, the approach would even allow us to unify the various pain scales (Scoville, Schmidt,

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text:
KIP, etc.) and assign a kind of universal valence score to different categories of pain and pleasure.1 That will be version 2.0. In the meantime, we thought to try to get a rough picture of the extreme joys and affections of members of the general public, which is what this article will focus on. Normal World vs. Lognormal World There is a world we could call the “Normal World,” where valence outliers are rare and most types of experiences affect people more or less similarly, distributed along a Gaussian curve. Then there is another, very different world we could call the “long-tailed world” or if we want to make it simple (acknowledging uncertainty) “Lognormal World,” where almost every valence distribution is a long-tail. So in the “Lognormal World,” say, for pleasure (and symmetrically for pain), we would expect to see a long-tail in the mean pleasure of experiences between different categories across all people, a long-tail in the amount of pleasure within a given type of experience across people, a long-tail for the number of times an individual has had a certain type of pleasure, a long-tail in the intensity of the pleasure experienced with a single category of experience within a single person, and so on. Do we live in the Normal World or the Lognormal World? Predictions of Lognormal World If we lived in the “Lognormal World,” we would expect: That people will typically say that their top #1 best/worst experience is not only a bit better/worse than their #2 experience, but a lot better/worse. Like, perhaps, even multiple times better/worse. That there will be a long-tail in the number of appearances of different categories (i.e., that a large amount, such as 80%, of top experiences will belong to the same narrow set of categories, and that there will be many different kinds of experiences capturing the remaining 20%). That for most pairs of experiences \(x\) and \(y\), people who have had both instances of \(x\) and \(y\), will usually agree about which one is better/worse. We call such a relationship a “deference.” More so, we would expect to see that deference, in general, will be transitive (\(a > b\) and \(b > c\) implying that \(a > c\)). To test the first and second prediction does not require a lot of data, but the third does because one needs to have enough comparisons to fill a lot of triads. The survey results we will discuss bellow are congruent with the first and second prediction. We did what we could with the data available to investigate the third, and tentatively, it seems to hold up (with ideas like deference network centrality analysis, triadic analysis, and tournament-style approaches). Survey Setup The survey asked the following questions: current level of pleasure, current level of pain, top 3 most pleasurable experiences (in decreasing order) along with pleasure ratings for each of them and the age when they were experienced, and the same for the top 3 most painful experiences. I specifically

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text:
did not provide a set of broad categories (such as “physical” or “emotional”) or a drop-down menu of possible narrow categories (e.g., going to the movies, aerobic exercise, etc.). I wanted to see what people would say when the question was as open-ended as possible. I also included questions aimed more directly at probing the long-tailed nature of valence: I asked participants to rate “how many times more pleasant was the #1 top experience relative to the #2 top experience” (and #2 relative to #3, and the same for the top most painful experiences). I also asked them to describe in more detail the single most pleasant and unpleasant experiences, and added a box for comments at the end in order to see if anyone complained about the task (most people said “no comment,” many said they enjoyed the task, and one person said that it made them nostalgic). I also asked about basic demographics (age and gender). Participants earned $1.75 for the task, which seems reasonable given the time it took to complete in most cases. Mechanical Turk: Participant Composition The survey was run on Mechanical Turk. I requested “Masters” qualifications for 90/110 of the survey responses. To be a Mechanical Turk Master(clickhappier 2016) you need to have a good track record of task approval, which I reasoned would increase the rate of well thought-out high-quality responses (this turned out to be true). The participants’ genders were fairly balanced (50/97 women, 47/97 men), and the average age was 36.5 years (sd = 10): Figure 7: Age distribution Bots (easy to spot–unless extremely sophisticated) While reading the responses I discovered that some of them seemed to be generated by bots. Apparently task requesters started noticing the presence of bots(Dreyfuss 2018) a couple of years ago. This is obviously a problem for academics trying to use the service for their research, and for machine learning professionals using the service for data-tagging. Having been both of those things in the past, I can say that a few years ago I did not see any submissions that looked suspiciously bot-like. Though low-quality rushed responses did seem to be relatively common back then, I never observed bot-like responses to open-ended questions. Unfortunately, this time I was able to spot several responses clearly written by bots. For example, one respondent answered the question “write a brief essay about your #1 best experience” with: The reason these types of assignments are given so often is that anyone can write about their own experience and it doesn’t require any outside resources or research. However, even though anyone can tell a story about their life, that does not mean anyone can write a good essay about that experience. As a professor and teacher for 30 years, I’ve read thousands of essays and can tell you there is a distinct difference from telling a story about yourself and writing an excellent personal experience essay. The difference between good and great: And it ends that way, with a colon indicating

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that the respondent is about to explain what the difference between good and great is. But it never does. In most cases the difference between a genuine response and a bot response was very obvious. That said, I erred on the side of caution for filtering bots and I got rid of answers even if they seemed just a little suspicious. This left me with 97 out of the 110 original responses. The following analysis was conducted on those 97 responses. Preprocessing Since the responses were open-ended I had to tag each of them with an experience category. To do this I read each response and identified the key theme in them and classified them with a label that was specific enough to distinguish it from nearby experiences (e.g., different types of fractures), but not so specific that we would never get more than one response per category (e.g., “breaking the middle finger in elementary school”). In general, most responses fell into very unambiguous categories (e.g. “When my father passed away” and “Watching my father die and take his last few breaths.” were both classified as “Father death”). About 10% of the responses were relatively ambiguous: it wasn’t clear what the source of the pain or pleasure was. To deal with those responses I used the label “Unspecified.” When some detail was present but ambiguity remained, such as when a broad type of pain or pleasure was mentioned but not the specific source I tagged it as “Unspecified X” where X was a broad category. For example, one person said that “broken bones” was the most painful experience they’ve had, which I labeled as “Unspecified fracture.” Results I should preface the following by saying that we are very aware of the lack of scientific rigor in this survey; it remains a pilot exploratory work. We didn’t specify the time-scale for the experiences (e.g., are we asking about the best minute of your life or the best month of your life?) or whether we were requesting instances of physical or psychological pain/pleasures. Despite this lack of constraints it was interesting to see very strong commonalities among people’s responses. Appearance Base Rates There were 77 and 124 categories of pleasure and pain identified, respectively. On the whole it seemed like there was a higher diversity of ways to suffer than of ways to experience intense bliss. Summoning the spirit of Tolstoy: “Happy families are all alike; every unhappy family is unhappy in its own way.” Here are the raw counts for each category with at least two appearances: Best experiences appearances (with at least two reports). Worst experience appearances (with at least two reports). For those who want to see the full list of number of appearances for each experience mentioned, see Appendix A (I also clarify some of the more confusing labels there too). A simple way to try to incorporate the information about the ranking is to weight experiences rated as top #1 with 3 points, those as top #2

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with 2 points, and those as the top #3 with 1 point. If you do this, the experiences scores are: Weighted appearances of best experiences (#1 – 3 points, #2 – 2 points, #3 – 1 point). Weighted appearances of worst experiences (#1 – 3 points, #2 – 2 points, #3 – 1 point). Average Ratings Given the relatively small sample size, I will only report the mean rating for pain and pleasure (out of 10) for categories of experience for which there were 6 or more respondents: For pain: 1. Father death (n = 19): mean 8.53, sd 2.3 2. Childbirth (n = 16): mean 7.94, sd 2.16 3. Grandmother death (n = 13): mean 8.12, sd 2.5 4. Mother death (n = 11): mean 9.4, sd 0.62 5. Car accident (n = 9): mean 8.42, sd 1.52 6. Kidney stone (n = 9): mean 5.97, sd 3.17 7. Migraine (n = 9): mean 5.36, sd 3.11 8. Romantic breakup (n = 9): mean 7.11, sd 1.52 9. Broken arm (n = 6): mean 8.28, sd 0.88 10. Broken leg (n = 6): mean 7.33, sd 2.02 11. Work failure (n = 6): mean 5.88, sd 3.57 (Note: the very high variance for kidney stones and migraine is partly explained by the presence of some very low responses, with values as low as 1.1/10 – perhaps misreported, or perhaps illustrating the extreme diversity of experiences of migraines and kidney stones). For pleasure: 1. Falling in love (n = 42): mean 8.68, sd 1.74 2. Children born (n = 41): mean 9.19, sd 1.64 3. Marriage (n = 21): mean 8.7, sd 1.25 4. Sex (n = 19): mean 8.72, sd 1.45 5. College graduation (n = 13): mean 7.73, sd 1.4 6. Orgasm (n = 11): mean 8.24, sd 1.63 7. Alcohol (n = 8): mean 6.84, sd 1.59 8. Vacation (n = 6): mean 9.12, sd 0.73 9. Getting job (n = 6): mean 7.22, sd 1.47 10. Personal favorite sports win (n = 6): mean 8.17, sd 1.23 Deference Graph of Top Experiences We will now finally get to the more exploratory and fun/interesting analysis, at least in that it will generate a cool way of visualizing what causes people great joy and pain. Namely, the idea of using people’s rankings in order to populate a global scale across people and show it in the form of a graph of deferences. While the scientific literature has some studies that compare pain across different categories(Spence, Miller, and Hendricks 1992)(Adams 1987)(Dolan 2011). I was not able to find any dataset that included actual rankings across a variety of categories. Hence why it was so appealing to visualize this. The simplest way of graphing experience deferences is to assign a node to each experience category and add an edge between experiences with deference relationships with a weight proportional to the number of directed deferences. For example, if 4 people have said that A was better than B, and 3 people

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text:
have said that B was better than A, then there will be an edge from A to B with a weight of 4 and an edge from B to A with a weight of 3. Additionally, we can then run a graph centrality algorithm such as PageRank(“Centrality” 2020) to see where the “deferences end up pooling.” The images below do this: the PageRank of the graph is represented with the color gradient (darker shades of green/red representing higher PageRank values for good/bad experiences). In addition, the graphs also represent the number of appearances in the dataset for each category with the size of each node: Best experiences deferences – edge thickness based on number of deferences, node size based on number of appearances, and color scheme based on PageRank. Worst experiences deferences – edge thickness based on number of deferences, node size based on number of appearances, and color scheme based on PageRank. The main problem with the approach above is that it double (triple?) counts experiences that are very common. Say that, for example, taking 5-MeO-DMT produces a consistently higher-valence feeling relative to having sex. If we only have a couple of people who report both 5-MeO-DMT and sex as their top experiences, the edge from sex to 5-MeO-DMT will be very weak, and the PageRank algorithm will underestimate the value of 5-MeO-DMT. In order to avoid the double counting effect of commonly-reported peak experiences we can instead add edge weights on the basis of the proportion with which an experience defers to the other. Let’s say that \(f(a, b)\) means “number of times that \(b\) is reported as higher than \(a\).” Then the proportion would be \(f(a, b) / (f(a, b) + f(b, a))\). Now, this introduces another problem, which is that pairs of experiences that appear together very infrequently might get a very high proportion score due to a low sample size. In order to prevent this we use Laplace smoothing and modify the equation to \((f(a, b) + 1) / (f(a, b) + f(b, a) + 2)\). Finally, we transform this proportion score from the range of \(0\) to \(1\) to the range of \(-1\) to \(1\) by multiplying by \(2\) and subtracting \(1\). We call this a “rebalanced smoothed proportion” \(w(a, b)\): \[w(a, b) = 2 \frac{f(a, b) + 1}{f(a, b) + f(b, a) + 2}-1\] I should note that this is not based on any rigorous math. The equation is based on my intuition for what I would expect to see in such a graph, namely a sort of confidenceweighted strength of directionality, but I do not guarantee that this is a principled way of doing so (did I mention this is a pilot small-scale low-budget ‘to a first approximation’ study?). I think that, nonetheless, doing this is still an improvement upon merely using the raw deference counts as the edge weights. To visualize what \(w(a, b)\) looks like I graphed its values for a and b in the range of \(0\) to \(20\)

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text:
(literally typing the equation into the google search bar): To populate the graph I only use the positive edge weights so that we can run the PageRank algorithm on it. This now looks a lot more reasonable and informative as a deference graph than the previous attempts: Best experiences deference graph: Edge weights based on the rebalanced smoothed proportions, size of nodes is proportional to number of appearances in the dataset, and the color tracks the PageRank of the graph. Edge color based on source node. Worst experiences deference graph: Edge weights based on the rebalanced smoothed proportions, size of nodes is proportional to number of appearances in the dataset, and the color tracks the PageRank of the graph. Edge color based on source node. By taking the PageRank of these graphs (calculated with NetworkX) we arrive at the following global rankings: PageRank of the graph of best experiences with edge weights computed with the rebalanced smoothed proportion equation. PageRank of the graph of worst experiences with edge weights computed with the rebalanced smoothed proportion equation. Intuitively this ranking seems more aligned with what I’ve heard before, but I will withhold judgement on it until we have much more data. Triadic Analysis With a more populated deference graph we can analyze in detail the degree to which triads (i.e. sets of three experiences such that each of the three possible deferences are present in the graph) show transitivity (cf. Balance vs. Status Theory). In particular, we should compare the prevalence of these two triads: Left: 030T, Right: 030C.(Batagelj and Mrvar 2001) The triads above are 030T, which is transitive, and 030C, which is a loop. The higher the degree of agreement between people and the higher the probability of the existence of an underlying shared scale, we would expect to see more triads of the type 030T relative to 030C. That said, a simple ratio is not enough, since the expected proportion between these two triads can be an artifact of the way the graph is constructed and/or its general shape (and hence the importance of comparing against randomized graphs that preserve as many other statistical features as possible). With our graph, we noticed that the very way in which the edges were introduced generated an artifact of a very strong difference between these two types of triads. In the case of pain there are 105 ‘030T,’ and 3 ‘030C.’ And for the pleasure questions there were 98 ‘030T,’ and 9 ‘030C.’ That said, many of these triads are the artifact of taking into account the top three experiences, which already generates a transitive triad by default when n = 1 for that particular triad of experiences. To avoid this artifact, we filtered the graph by only adding edges when a pair of experiences appeared at least twice (and discounting the edges where w(a, b) = 0). With this adjustment we got 2 ‘030T,’ and 1 ‘030C’ for the pain questions, and 1 ‘030T,’ and 0 ‘030C’ for the pleasure

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text:
question. Clearly there is not enough data to meaningfully conduct this type of analysis. If we extend the study and get a larger sample size, this analysis might be much more informative. Latent Trait Ratings A final approach I tried for deriving a global ranking of experiences was to assume a latent parameter for pain or pleasure of different experiences and treating the rankings as the tournament results of participants with skill equal to this latent trait. So when someone says that an experience of sex was better than an experience of getting a new bike we imagine that “sex” had a match with “getting bike” and that “sex” won that match. If we do this, then we can import any of the many tournament algorithms(Mathieu and Vladu 2011) that exist (such as the Elo rating system(“Elo Rating System” 2020)) in order to approximate the latent “skill” trait of each experience (except that here it is the “skill” to cause you pleasure or pain, rather than any kind of gaming ability). Interestingly, this strategy has also been used in other areas outside of actual tournaments, such as deriving university rankings based on the choices made by students admitted to more than one college (see: Revealed Preference Rankings of US Colleges and Universities). I should mention that the fact that we are asking about peak experiences likely violates some of the assumptions of these algorithms, since the fact that a match takes place is already information that both experiences made it into the top 3. That said, if the patterns of deference are very strong, this might not represent a problem. To come up with this tournament-style ranking I decided to go for a state-of-the-art algorithm. The one that I was able to find and use was Microsoft Research’s algorithm called TrueSkill (which is employed to rank players in Xbox LIVE). According to their documentation, to arrive at a conservative “leaderboard” that balances the estimated “true skill” and the uncertainty around it, they recommend ranking by the expected skill level minus three times the standard error around this estimate. If we do this, we arrive at the following experience “leaderboards”: Conservative TrueSkill scores for best (left) and worst (right) experiences (mu – 3*sigma). Long-tails in the Responses to “How Many Times Better/Worse” Question The survey included four questions aimed at comparing the relative hedonic values of peak experiences: “Relative to the 1st most pleasant experience, how many times better was the 2nd most pleasant experience?” (This was one, the other three were the permutations of also asking about 2nd vs. 3rd and about the bad experiences): (Note: I’ll ignore the responses to the comparison between the 2nd and 3rd worst pains because I messed up the question - I forgot to substitute “better” for “worse”). I would understand the skepticism about these graphs. But at the same time, I don’t think it is absurd that for many people the worst experience they’ve had is indeed 10 or 100 times worse than

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