Value of Holding Money

Conceptual Framework: Epistemic Uncertainty and Virtual Organizations

Research prioritization faces a fundamental epistemic uncertainty: there are funding opportunities that we don't know of yet, and that we may discover (or that may start to exist) later on. This uncertainty adds some potential value to holding money rather than allocating all available funds to known funding opportunities.

To account for this epistemic uncertainty, we use the concept of virtual organizations - hypothetical funding opportunities that represent the expected value of newly discovered funding opportunities we don't know of yet. By including virtual organizations in our modeling, we aim to represent the expected value of holding money for future opportunities.

There are two main parameters that control virtual organization creation:

VirtualOrgsSamplingStrategy: Configures how virtual organizations are sampled from existing organization expected values
VirtualOrgsPerYear: Specifies how many virtual organizations to add each year

Both parameters are located in the meta tab of the input spreadsheet.

Technical Implementation: Virtual Organization Creation Process

The virtual organizations sampling process is repeated for each year starting from year 2 (future years), with virtual organizations being prolonged to subsequent years using median discounting. Year 1 represents the present year with only real organizations.

Step 1: Extract Expected Values for Year i

The system starts with the Expected Value (EV) matrix for year i. Each "world" or "simulation" is considered independently. For simulation_1, we extract organisation EVs: \(EV_{i,sim1}\)

Year i EV Matrix:

Simulation	Org A	Org B	Org C	Org D	...
simulation_1	0.8	0.3	0.9	0.5	...
simulation_2	0.6	0.7	0.2	0.9	...
simulation_3	0.9	0.4	0.8	0.3	...
...	...	...	...	...	...

Step 2: Sample Virtual Organizations for Year i

We sample from \(EV_i\) using the chosen sampling strategy for as many organizations as specified by VirtualOrgsPerYear.

The sampling methods are detailed in the section Sampling Strategies.

Step 3: Add Virtual Organizations to Year i

Virtual organizations are added to the EV matrix for year i with newly generated values:

Year i EV Matrix (with Virtual Orgs):

Simulation	Org A	Org B	Org C	Org D	VirtualOrg1	VirtualOrg2	...
simulation_1	0.8	0.3	0.9	0.5	0.7	0.4	...
simulation_2	0.6	0.7	0.2	0.9	0.8	0.6	...
simulation_3	0.9	0.4	0.8	0.3	0.5	0.9	...
...	...	...	...	...	...	...	...

Step 4: Prolong Virtual Organizations to Subsequent Years

Virtual organizations created in year i are prolonged to subsequent years (i+1, i+2, etc.) using the median discount rate. The median discount rate is calculated from all organizations' discount rates in the system.

Discount Rate Calculation:

Organization	Discount Rate
Org A	0.05
Org B	0.03
Org C	0.07
Org D	0.04
Median	0.045

Note: In typical cases, all organizations will have similar discount rates, so the median provides a representative rate for all organizations.

Year i+1 EV Matrix (with Prolonged Virtual Orgs):

Simulation	Org A	Org B	Org C	Org D	VirtualOrg1	VirtualOrg2	...
simulation_1	0.76	0.29	0.86	0.48	0.67	0.38	...
simulation_2	0.57	0.67	0.19	0.86	0.76	0.57	...
simulation_3	0.86	0.38	0.76	0.29	0.48	0.86	...
...	...	...	...	...	...	...	...

Note: All organization values (real and virtual) are discounted by the median discount rate (0.045) from year i to year i+1

Step 5: Repeat Process for Each Year

This entire process (Steps 1-4) is repeated for each year starting from year 2. Year 1 represents the present year with only real organizations.

Year 1 (Present): Only real organizations exist
Year 2: Extract EVs → Sample virtual orgs → Add to matrix → Prolong to Year 3
Year 3: Extract EVs → Sample virtual orgs → Add to matrix → Prolong to Year 4
Year 4: Extract EVs → Sample virtual orgs → Add to matrix → Prolong to Year 5
...and so on for all future years

Multi-Year Virtual Organization Timeline:

Year	Description	Virtual Orgs Added	Virtual Orgs from Previous Years	Total Virtual Orgs
1	Present	0	0	0
2	Future	2	0	2
3	Future	2	2 (discounted)	4
4	Future	2	4 (discounted)	6
5	Future	2	6 (discounted)	8
...	...	...	...	...

Step 6: Final Multi-Year EV Matrix

The final EV matrix contains all real organizations plus all virtual organizations across all years, with virtual organizations properly discounted for each year they appear in.

Sampling Strategies

Each strategy combines two dimensions: how values are generated (sample vs percentile) and whether we fit a distribution or use empirical data; plus whether weights are used.

Strategy	Mode	Fit	Weighted
`fit_sample`	sample	Yes	No
`fit_percentile`	percentile	Yes	No
`percentile`	percentile	No	No
`weighted_fit_sample`	sample	Yes	Yes
`weighted_fit_percentile`	percentile	Yes	Yes
`weighted_percentile`	percentile	No	Yes

Fit Sample (`"fit_sample"`)

Fits candidate distributions (lognormal, gamma, normal) to \(EV_{i,sim}\)
Uses Kolmogorov-Smirnov to select the best fit
Draws n random samples from the fitted distribution

Fit Percentile (`"fit_percentile"`)

Fits as above, then returns n evenly spaced interior percentiles from the fitted distribution
Deterministic for given inputs; useful for stable, representative points

Percentile (`"percentile"`)

Takes actual percentiles from the existing organization data (empirical)
For n=1: 50th percentile; n=2: ~33rd/66th; n=3: 25th/50th/75th
Fast and preserves the empirical shape

Weighted Fit Sample (`"weighted_fit_sample"`)

Like fit_sample, but uses room for funding as weights when fitting
Emphasizes organizations with higher funding capacity

Weighted Fit Percentile (`"weighted_fit_percentile"`)

Like fit_percentile, but uses room for funding as weights when fitting
Returns percentiles of the weighted fitted distribution

Weighted Percentile (`"weighted_percentile"`)

Like percentile, but computes percentiles using room for funding as weights
With equal weights, matches percentile

Implementation

The sampling strategies are implemented in draw_samples.R.