Is LiOH a weaker base than NaOH? Is $\ce{LiOH}$ a weaker base than $\ce{NaOH}$?

Note: I'm not interested in "why," but rather what the "real" $\mathrm{p}K_
\mathrm{b}$ values are. 

$$
\begin{array}{lcc}
\text{Data for Alkali Metal Hydroxides} \\
\hline
\text{Cation} &amp; \mathrm{p}K_\mathrm{b} &amp; \text{Solubility} &amp; \text{Solubility} \\
\text{} &amp; \text{} &amp; \pu{g/100 ml} \text{ at } \pu{20 ^\circ C} &amp; \pu{moles/L} \text{ at } \pu{20 ^\circ C} \\
\hline
\ce{Li} &amp; -0.36 &amp; 12.8 &amp; 5.34\\
\ce{Na} &amp; 0.2 &amp; 111 &amp; 27.75\\
\ce{K} &amp; 0.5 &amp; 112 &amp; 20.0  \\
\ce{Rb} &amp; ? &amp; 180 &amp; 17.6\\
\ce{Cs} &amp; -1.76 &amp; 200? &amp; 13.3?\\
\hline
\end{array}
$$

The $\mathrm{p}K_\mathrm{b}$ data is from Wikipedia ($\ce{Li}$, $\ce{Na}$, $\ce{K}$, and $\ce{Cs}$). Wikipedia doesn't have a value for $\ce{Rb}$ and I couldn't find one.     

The solubility data is from the Wikipedia Solubility Table. Wikipedia doesn't have a solubility value for $\ce{CsOH}$ at $\pu{20 ^\circ C}$  and I couldn't find one, About $\pu{200 g}$ would be a reasonable guess, which would be $\pu{13.3M}$.

One point is that the Wikipedia article for lithium hydroxide says "It ... is the weakest base among the alkali metal hydroxides." 

Another point is an earlier question "Why is $\ce{LiOH}$ a weaker base than $\ce{NaOH}$". User Lighthart references a paper "Ions in water: The microscopic structure of concentrated hydroxide solutions" by Imberti et al. but the abstract at least doesn't seem to address the strength of the alkali hydroxides directly (I don't have access to the paper itself since it is behind a paywall).

Is this one of the Bertrand Chord paradox problems where it depends on how we define "stronger"?


With a $\mathrm{p}K_\mathrm{b}$ of -0.36, $\ce{LiOH}$ would seem to be a stronger base than either $\ce{NaOH}$ or $\ce{KOH}$.
Certainly more moles of $\ce{NaOH}$ dissolve in a liter of solution at $\pu{20 ^\circ C}$ than any other alkali hydroxide. 


EDIT 3/22/2016 11:31 pm

Found a different table of $\mathrm{pK}_\mathrm{b}$ data for the alkali hydroxides: Source-2 

EDIT 3/23/2016 12:12 am
Source-3 CRC Handbook of Chemistry and Physics, 92nd edition, "Dissociation Constants of Inorganic Acids and Bases. Only $\ce{Li}$ $(\mathrm{p}K_\mathrm{a}= 13.8)$ and $\ce{Na}$ $(\mathrm{p}K_\mathrm{a}=14.8)$ are listed as $\mathrm{p}K_\mathrm{a}$ of the cations. It is the same data as in this pdf file which is from another edition.

$$
\begin{array}{lcc}
\hline
\text{Cation} &amp; \text{Wikipedia} &amp; \text{Source-2} &amp; \text{CRC}\\
\hline
\ce{Li} &amp; -0.36 &amp; 0.18 &amp; 0.2 \\
\ce{Na} &amp; 0.2 &amp; -0.56 &amp; -0.8 \\
\ce{K} &amp; 0.5 &amp; -1.1 &amp; \\
\ce{Rb} &amp; ? &amp; -1.4 &amp; \\
\ce{Cs} &amp; -1.76 &amp; -1.76 &amp; \\
\hline
\end{array}
$$
In Proton Affinities of the Alkali Hydroxides J. Am. Chem. Soc., 1969, 91, pp 2810–2811, it is shown that gas phase affinities in $\pu{kcal/mol}$ are:  


  
  $\ce{LiOH}$: 240.7
  $\ce{NaOH}$: 247.6
  $\ce{KOH}$: 262.6 
  $\ce{CsOH}$: 269.2
  


So, yes, $\ce{LiOH}$ is weaker, at least in the gas phase.   

In aqueous solution, ACIDITY FUNCTIONS FOR STRONGLY BASIC SOLUTIONS Chemical Reviews volume 66, pages 119-131:  


  the order of basicity for the same molarity of aqueous solution, $\ce{LiOH &lt; NaOH &lt; KOH}$. 


For example, for a $\pu{1M}$ solution, the acidity function (H) is: 


  
  $\ce{LiOH}$: 13.48
  $\ce{NaOH}$: 14.01, 14.16 (two different measurement techniques)
  $\ce{KOH}$: 14.17
  


So in both the gas and aqueous phases, $\ce{LiOH}$ is a weaker base than $\ce{NaOH}$.