In certain non-catalytic reactions that diastereomer will predominate, which could be formed by the approach of the entering group from the least hindered side when the rotational conformation of the C-C bond is such that the double bond is flanked by the two least bulky groups attached to the adjacent asymmetric center.
The rule indicates that the presence of an asymmetric center in a molecule induces the formation of an asymmetric center adjacent to it based on steric hindrance.
In his 1952 publication Cram presented a large number of reactions described in the literature for which the conformation of the reaction products could be explained based on this rule and he also described an elaborate experiment (scheme 1) making his case.
The experiments involved two reactions. In experiment one 2-phenylpropionaldehyde (1, racemic but (R)-enantiomer shown) was reacted with the Grignard reagent of bromobenzene to 1,2-diphenyl-1-propanol (2) as a mixture of diastereomers, predominantly the threo isomer (see for explanation the Fischer projection).
The preference for the formation of the threo isomer can be explained by the rule stated above by having the active nucleophile in this reaction attacking the carbonyl group from the least hindered side (see Newman projection A) when the carbonyl is positioned in a staggered formation with the methyl group and the hydrogen atom, which are the two smallest substituents creating a minimum of steric hindrance, in a gauche orientation and phenyl as the most bulky group in the anti conformation.
The second reaction is the organic reduction of 1,2-diphenyl-1-propanone 2 with lithium aluminium hydride, which results in the same reaction product as above but now with preference for the erythro isomer (2a). Now a hydride anion (H-) is the nucleophile attacking from the least hindered side (imagine hydrogen entering from the paper plane).
^ Studies in Stereochemistry. X. The Rule of “Steric Control of Asymmetric Induction” in the Syntheses of Acyclic Systems Donald J. Cram, Fathy Ahmed Abd Elhafez J. Am. Chem. Soc.; 1952; 74(23); 5828–5835. Abstract