[NOTE - the original version is interactive, it is recommended to read there and comment here]

This is a representation of ideas from The elephant in the bednet: the importance of philosophy when choosing between extending and improving lives (and relevant discussion), by Michael Plant, Joel McGuire^[1], and Samuel Dupret. No new ideas are presented here, it is only intended to present visuals and hopefully clarify and explain the general concepts.

It starts with a basic example of a possible life change (or 'intervention') that affects personal wellbeing (getting a dog) in order to introduce a visualisation of wellbeing measurement and define what is meant by a WELLBY. It then uses the same visual structure to look a life-saving interventions and shows three different ways to account for the badness of death. For two of these the definition of a 'neutral point' is important, and this is also visualised.

Based on suggestions from the original authors, the effect of progress on expected wellbeing, and the holding of a weighted combination of different accounts of death are also investigated.

It does not go into detail on the philosophical arguments for different views or use these views to look at charity cost-effectiveness. For these and more detail the reader is referred to the original post.

All ideas originate with the original authors, and any inaccuracies or inconsistencies are likely introduced by myself (please comment if any errors are found).

Visualising wellbeing

Consider a 25 year-old who had a good childhood, where they would rate their own wellbeing as $\frac{8}{10}$. Perhaps they then had some rocky teenage years that they would rate as $\frac{6}{10}$, but after this they levelled off at a decent enough life, where they would say their wellbeing was $\frac{7}{10}$. We can graph their subjective rating of wellbeing to-date (―), along with the expectation that this level of wellbeing will continue into the future in the absence of any major life changes ($—$). The area underneath this line ($▉$) is then defined as the number of wellbeing-adjusted life years (WELLBYs) gained to a certain age.

Suppose that this person is now considering the possibility of getting a pet dog. They like dogs and expect that it will increase their personal wellbeing by one point (to $\frac{8}{10}$​) for its ten year life ($\text{– –}$); however, having a dog will prevent them from taking a year off aged 30 to travel abroad, which they would otherwise have rated as $\frac{10}{10}$​ for wellbeing.

Looking at the WELLBYs provided by the intervention of getting a dog, we can see that (all else being equal) the dog would provide 9 positive WELLBYs ( $▉$,) and 2 negative ( $▉$) ; overall giving an increase over the baseline of 7 WELLBYs, and therefore being a good choice for this person.

Accounting for the badness of death

Adding up the change in WELLBYs for most life-changing interventions is straightforward. However, in order to compare WELLBYs for life-saving interventions we are forced to consider how many WELLBYs are generated by remaining alive, which depends on the philosophical approach we take. Three possible views we could take are Epicureanism, Deprivationism, or a Time-relative interest account.

Epicureanism

This takes the view that being dead is not bad for the dead person, as they have no subjective experience of being dead.

If we consider a life-saving intervention for a 10 year old person, it might be able to give them continued existence to a life expectancy of 70 years, but under an Epicurean view we wouldn't count this as providing any WELLBYs, as they are no better off than if they were dead.

Deprivationism

This views the badness of death as the difference between the wellbeing you actually had compared to how much you would have had if you’d lived longer. So giving 60 years extra life to the same person with an expected wellbeing of $\frac{6}{10}$​ would provide 360 WELLBYs.

Time-relative interest account (TRIA)

This view considers that the badness of death depends on the age at which a person dies. Under this view the WELLBYs gained from a life-saving intervention increase from zero at birth (similar to an Epicurean view) through to the full value of expected wellbeing at some set age (similar to a Deprivationist view). This age is defined as the age at which a person is considered fully 'psychologically connected' to their later self.

For example, if the age of full psychological connectedness is 20, and our life-saving intervention happens at age 10, then the WELLBYs gained are 50% of the total possible. If our expected level of wellbeing is $\frac{6}{10}$​ then the WELLBYs claimed from the intervention would be 3 per year, or 180 WELLBYs over their expected lifespan.

The effect of connectedness age, versus the age at which the life is saved, may be investigated interactively in the original post.

Another way to think about TRIA is to consider the years of life lost due to death at a certain age. TRIA is equivalent to a Deprivationist view if the age of connectedness is zero, in which case the years of life lost by a death immediately after birth are the full expected lifespan of the person, linearly decreasing for death at older ages. With a higher age of connectedness a death in the years up to connectedness discounts the years of life lost.

The neutral point

For the Deprivationist and TRIA approach we have assumed above that death equates to a wellbeing level of zero, however it can be argued that low levels of wellbeing don't represent lives worth living, and therefore the 'neutral point' is some value above this. We can define this neutral point as the level at which continued existence would be overall neither good nor bad for the person. WELLBYs are therefore only gained relative to this level and its definition has a significant impact on the expected benefits of any given intervention.

The effect of the neutral point on number of WELLBYs, alongside intervention age, connectedness age, expected lifespan and expected wellbeing level can be investigated interactively in the original post.

Under the conditions above, 90 WELLBYs are gained by the life-saving intervention (the green area $▉$, minus the red area $▉$).

The effect of progress

The above analysis assumes an expected wellbeing level that is fixed for the remainder of a person's life. In practice, our expectation may be that wellbeing will either increase or decrease over a persons lifetime, based on things like ailing personal health or improved standards of living in their area. We can take into account an expected increase or decrease in expected wellbeing, per decade, from the point of our intervention; this adds a gradient to our expectation line. (interactive in original post)

With expected wellbeing changing, the estimate is now 134.2 WELLBYs gained by the life-saving intervention.

Holding a combination of views

Above we looked three different philosophical viewpoints on the wellbeing gained from a life-saving intervention: Epicureanism, Deprivationism, and a Time-relative interest account (TRIA). For both the Deprivationist and TRIA viewpoints it is necessary to define a neutral point (the wellbeing level at which continued existence would be neither good nor bad) and an expected wellbeing level, that could be increasing or decreasing through the person's lifetime.

Philosophers disagree on what viewpoint is 'correct', and so one option for calculating WELLBYs is to take some form of average across all views, weighted your own personal credence in each being right. With all the values stated above (neutral point, connectedness age, wellbeing change over time, etc), the effect of changing the weighting on each view can be explored below.

The weighted combination of... (interactive in original post)

20% Epicureanism (being dead is not bad for the dead person) : no WELLBYs

60% TRIA (Time-relative interest account - WELLBYs lost depend on the age at which a person dies) : 134.2 WELLBYs

20% Deprivationism (all potential wellbeing is lost - WELLBYs lost equal to a full life) : 268.5 WELLBYs

... would give (0.2×0 + 0.6×134.2 + 0.2×268.5 = ) 134.2 WELLBYs gained by the life-saving intervention.

1. ^{^}

   Thanks to Joel for his encouragement and suggestions for minor improvements to this.