Survey Statistics: toy example for energy balancing weights

Last week we talked about The Big Changes Coming to the Times/Siena Poll: New weighting variable: support score = E(2024 vote | other X variables). New weighting method: energy balancing (Huling & Mak, 2024) Ben Schneider helpfully blogged about energy balancing as well: Raking and similar calibration methods are based on balancing means or totals for specific variables…The energy balancing method does something different: it calibrates based on an entire multivariate distribution, as measured by an empirical cumulative distribution function (ECDF). Jared Huling (of Huling & Mak, 2024) helpfully answered questions in the comments. I’m still puzzling over how energy balancing handles empty cells (unsampled regions of the joint covariate space). I need a toy example. Consider 2 binary variables, so 4 population cells, with known population shares: k=0 k=1 total j=0 .4 .2 .6 j=1 .2 .2 .4 total .6 .4 Say the sample is missing folks in cell 11: k=0 k=1 total j=0 .5 .3 .8 j=1 .2 0 .2 total…